One night Yogi Bear, Boo-Boo, Cindy, Huckleberry Hound, Snagglepuss, Wally Gator, Quick Draw McGraw, Baba Looey, Magilla Gorilla, Peter Potamus, So-So, Top Cat, Benny the Ball, Choo-Choo, Spook, Fancy-Fancy, Brain, Augie Doggie and Doggie Daddy, Squiddly Diddly, Atom Ant, Yakky Doodle, Snooper and Blabber, Lippy the Lion and Hardy Har Har, Touche Turtle and Dum-Dum and Ricochet Rabbit and Droop-a-Long arrive in London, England at night. Meanwhile when Sophie can't sleep during the 'witching hour', she looks out of her window of her dormitory and sees a cloaked giant blowing something into a bedroom window down the street. The giant sees her, and although she tries to hide in her bed, he reaches through the window and carries her, along with Yogi and his gang, to his home.
Fortunately for Sophie and Yogi and the gang, they have been abducted by the world's only good giant, the Big Friendly Giant (or BFG). Operating in the strictest secrecy, the BFG catches dreams (which manifest themselves in Dream Country as floating semi-fluid sparkler-like objects) and at night, he blows his bottled dreams into the bedrooms of children. The other, larger giants are vicious, cannibalistic monsters; they go out into the world to steal and eat humans, mostly children, since there is little else for them to eat where they live. Because the BFG refused to eat people, he must survive on a revolting vegetable known as a snozzcumber, and thus the other giants regard him with contempt. Sophie, Yogi and the gang and the BFG form a quick bond, and the BFG develops a paternal sentiment for them. However, Sophie's life is put in danger by the sudden arrival of the Bloodbottler Giant, one of the fearsome flesh-eating giants who live in the wastes outside the BFG's house. The giant demands to know who the BFG is talking to, but the BFG lies telling him he is talking to himself. The Bloodbottler (correctly) assumes the BFG is talking to a human and begins searching for Sophie so he can eat her.
Sophie hides in the snozzcumber, but unknown to the BFG, and the BFG offers the snozzcumber to the Bloodbottler hoping its foul taste will send the monster hollering out of the cave and leave him in peace. The Bloodbottler crunches up the snozzcumber, but luckily spits Sophie out. In a rage, the beast destroys the cave and storms out. The BFG helps Sophie recover, makes her a new dress and treats her and the others to a strange, but delicious fizzy drink called frobscottle. It is rather unusual in that the bubbles in the drink travel downwards and therefore cause the drinker to break into loud flatulence instead of burping: this is known as a Whizzpopper, which causes the drinker of the frobscottle to fly. After this the BFG takes Sophie and Yogi and the gang to Dream Country to catch more dreams he calls Phizzwizards, but is tormented by the other giants along the way, notably their leader, the Fleshlumpeater, the largest and most fearsome giant of all. Dick Dastardly and Muttley are also there, working for the giants. After escaping them and arriving in Dream Country, the BFG demonstrates his dream-catching skills to Sophie and Yogi and the gang, but is unlucky enough to catch a Trogglehumper, which is essentially a particularly horrific nightmare.
Back at the BFG's cave, he shows Sophie and Yogi and the others the huge storeroom where he keeps all the dreams he has captured over the years. He even takes Sophie and Yogi and the others with them to watch him on his dream-blowing duties, but this is cut short when they spot the Fleshlumpeater about to feast on one of the children that the BFG had blown a dream to. Sophie cries out, attracting the Fleshlumpeater's attention and forcing the BFG to flee.
Sophie and Yogi and the gang persuade the BFG that something must be done the destory the evil giants, even if it means getting the word out. At first, the BFG is reluctant to do so, since he views all adult humans as bad people, but Sophie and Yogi and the gang manage to convince him otherwise. Together, they develop a plan to get the Queen of the United Kingdom to help them. Using dreams from his collection, the BFG mixes up a terrible nightmare that will show the Queen what the giants do. They set off for Buckingham Palace and blow the dream into the Queen's bedroom. The BFG then leaves Sophie, Yogi Bear, Boo-Boo, Cindy, Quick Draw McGraw, Baba Looey, Snagglepuss, Huckleberry Hound, Augie Doggie and Doggie Daddy and Snooper and Blabber on the Queen's windowsill while Top Cat, Benny the Ball, Choo-Choo, Spook, Fancy-Fancy, Brain, Magilla Gorilla, Wally Gator, Peter Potamus, So-So, Squiddly Diddly, Atom Ant, Yakky Doodle, Lippy the Lion and Hardy Har Har, Touche Turtle and Dum-Dum and Ricochet Rabbit and Droop-a-Long go to get some help from Yogi's old friends. Then the BFG retreats into the palace gardens.
When the queen awakens, Sophie convinces her that all of her dream was true. Because the dream included the knowledge that Sophie and the others would be there when she woke up, the Queen believes them and speaks with the BFG. After considerable effort by the palace stuff, the BFG is given a lavish breakfast and the Queen summons the Head of the Army and the Marshall of the Air Force to begin work on neutralizing the evil giants. Top Cat and the others who have gone for help then return with Fred Flintstone and Barney Rubble.
Eventually a huge fleet of RAF Chinook helicopters follow the BFG to the giants' homeland. While the child-eating giants are asleep, the Army tie them up, planning to hang them under several helicopters each, and transport them to London, where a special large pit has been constructed from which they will not be able to escape. However the giants are disturbed and begin to wake up, causing chaos and several soldiers to be injured. Eventually the giants attempt to free themselves from the chains that bind them, resulting in them being knocked out, and peace is momentarilly restored. The only one who escapes being trapped is the Fleshlumpeater, who immediately goes after the BFG, who decides to face the Fleshlumpeater despite knowing he will stand no chance against him. Infuriated at being betrayed, the Fleshlumpeater is about to kill the BFG and Yogi and the gang when Sophie screams out. Hearing this, the Fleshlumpeater drops the BFG and prepares to eat Sophie, Quick Draw McGraw, Snagglepuss and Wally Gator alive, but after a long struggle he is finally subdued with the nightmare-including Trogglehumper BFG caught earlier, and is carried away with the rest but not before Dick Dastarldly and Muttley are blasted back into space. The BFG then mentions that the Trogglehumper was a dream about a legendary giant killer called Jack.
As a punishment for their lifetimes of child-eating, the giants are placed in the pit and forced to eat snozzcumbers for the rest of their lives, fed to them by the awful Mrs. Clonkers who ran the orphanage Sophie lived in, resulting in its closure. Afterwards, the Queen offers Sophie a place to stay in her palace along with all the other girls from the orphanage. The BFG is offered a castle to live in, but instead decides to continue his duty of blowing dreams for children. Sophie cannot bear to part from the BFG, so she decides to remain with him hear after. They toghether fly back to Giant Country, while Yogi and his gang look for a new adventure and Fred and Barney say 'Made you look!'.