The man scaled an outer perimeter fence near Lincoln and Sepulveda boulevards Monday shortly after 2 p.m.
Officers spotted the man climb the fence and took him into custody as he appeared to be getting closer to a Delta plane that was staging for departure.
One passenger on the Delta flight said it appeared the man was doing pushups before he was apprehended.
Police say the man appears to be a transient with mental health issues and who had no identification. He is expected to be taken to a mental-health facility for an evaluation.