If George and Lennie are protagonists in Of Mice and Men, Curley would have to be seen as an antagonist in Steinbeck's work.
Curley is the son of the boss of the ranch. He is a former boxer who was quite successful in the ring. He has a sense of entitlement. Candy notes that he's a "small guy" and because he is so small, he likes to pick fights with men who are bigger than him. When Candy describes him in chapter 2, he makes the argument to George that Curley is in a no-lose situation. If the bigger guy beats him up, he will receive public scorn because he fought someone smaller than him. If Curley prevails, then it goes to show his talent.
Curley's size helps foster his defensive attitude. This is shown in his initial interaction with Lennie in chapter 2, and how he challenges Lennie to a fight in chapter 3. This leads Lennie to strike back and break Curley's hand, fueling a particular vengeance that is evident when Curley leads the lynch party to kill Lennie at the end of the book. When Curley finds George with the dead Lennie, Curley wants to know how it happened and seems to speak with an almost joyously savoring tone at the sight of the dead body.
There are some indications that Curley is not very understanding toward his wife. Curley's wife says that Curley's "not a nice fella" and she immediately runs off when she hears that he is looking for her. Curley is distinctive because he wears a black glove that is reputed to contain Vaseline so that his hand can be “soft” for his wife. In contrast to the depth of Slim or George at the end of the novella, Curley is fairly superficial in terms of how he views life. He cares about himself and satisfies his needs. This can be seen at the end of the novel when he and Carlson look at Slim and George and wonder what is wrong with them.