Bouncing/jumping during acceleration

I'm having a problem with a bouncing sensation, kind of like if I were driving on a bumpy road, when I'm accelerating at high speeds and/or when acceleration requires a lot of power (i.e. accelerating uphill). It does NOT do it when I accelerate normally from a stop, but I can feel that it's accelerating differently than normal.

My mechanic at work suggested it might be the fuel filter, the fuel pump, or maybe my spark plugs. I have already changed the fuel filter hoping that that would solve the problem, but it didn't. I plan on replacing the fuel pump or plugs next.

Is there anything else that could be causing this problem?