Oblivious to Billy's limitless hunger, the wolf gives him a bottle of milk, but Billy spills the milk and eats the bottle, the pacifier, the cutlery and crockery (like a sandwich), the coffeepot (along with all the coffee inside it), and the napkin.
Realizing that Billy will be more than a handful to deal with, the wolf tries to tie him in the garden to a hook hammered into the ground, but Billy eats the rope and comically eats the top part of the wolf's shoe when he tries to stop him.
Even this isn't enough to satisfy the little goat, as Billy then eats the moon, taking the moonlight along with it and leaving the Earth in darkness.
Billy Boy is the first solo cartoon Tex Avery directed featuring his southern-wolf character, who previously appeared with Droopy in The Three Little Pups and later in Blackboard Jumble and Sheep-Wrecked.
The short was originally planned as a Barney Bear cartoon with Dick Lundy as the director, but was changed when Avery returned after a sabbatical.