From Longman Dictionary of Contemporary Englishbig-headedbig-head‧ed /ˌbɪɡˈhedɪd◂/ ●○○ adjective informalBOAST someone who is big-headed thinks they are very important, clever etc – used to show disapproval OPP modest► see thesaurus at proud —big-head noun [countable]
Examples from the Corpus
big-headed• But later, I realized that it had been quite good for me and stopped me getting big-headed.• I see now that it was just his way of keeping me on my mettle and making sure I didn't get big-headed.• I don't want to seem big-headed but I frankly don't think it will work.• I don't want to sound big-headed, but I thought my picture was the best.• I suppose that might be a fear of being considered big-headed or vain.• The big-headed silhouette with its strangely twisted mandibles surprises motorists on a day out to the seaside.• Better than being big-headed, the thing Uncle Max was always slapping me down for. 