a big head

1. An exaggerated sense of one's importance or status. Often used with the verbs "get" or "have." Jeff has such a big head now that he's captain and thinks he's in charge of everything. Susan got a big head for a while after her promotion, but she's been more modest recently.

2. A conceited person who exaggerates his or her own importance or skillfulness. Bill is such a big-head and thinks he's smarter than everyone else just because he has his PhD.