大きな顔をする　To Look as if One is Important; Puffed Up

大おおきな顔かおをする　To look as if one is important; puffed up

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Said when someone is overly proud (and the speaker thinks that he should be more humble).
Literally, “to make one’s face large.” Having a large face means people are more likely to take notice of you.

彼かれはまだ新入社員しんにゅうしゃいんなのに、もう大おおきな顔かおをしている。

Although he’s still a new employee, he sure acts like a big shot.

彼かれ—he
まだ—still (only a new employee)
新入社員しんにゅうしゃいん—new employee
[lit: 新しん (new); 入にゅう (enter); 社しゃ (company); 員いん (member)]
なのに—although; in spite of the fact…
もう—already