In "The BFG", the main character, Sophie, is a young orphan who gets kidnapped by the BFG (Big Friendly Giant).
The BFG doesn't "hunt" anything in the typical sense. He is a gentle giant who collects dreams and delivers them to sleeping children. He does, however, hunt for snozzcumbers, which are a type of vegetable he enjoys eating.
Perhaps you are remembering a scene from the book where Sophie and the BFG go on an adventure to catch a "dream" for her to see. He uses a special net to capture dreams, and you could say that he is "hunting" for them.
Do you remember any more details about the book or what you are thinking of? That could help clarify!