An oxymoron. Before one receives a degree, one is an undergraduate (has not graduated). Upon receiving a degree that person becomes a graduate, therefore one can't hold a degree and be an undergraduate. Degrees earned after ones bacelor degree are called graduate degrees, which seems to have led to the mistaken notion that a bachelor degree should be called an "undergraduate degree".
He graduated last year with an undergraduate degree.
by grammarnut December 13, 2010