Adjective: bigheaded ,big'he-did
- Overly conceited or arrogant; showing or characterized by a superior, disdainful, or haughty attitude
"His bigheaded behaviour after winning the award annoyed his colleagues";
- snooty [informal], snot-nosed [informal], snotty [informal], stuck-up [informal], too big for one's breeches [informal], uppish [informal], pernickety [Brit, informal], snobbish
See also: proud, toffee-nosed [Brit, informal]