I have two answers depending on whether you have your exposure on manual, or auto. With the dial on movie, press MENU and choose the two-dot movie tab. Is movie exposure manual or auto?
Manual: in manual mode, you need to actually set your shutter speed aperture, and ISO. (Jog wheel, Av+jog wheel and ISO button.) The answer is simply that you didn't choose a combination that gave you the correct exposure. Half press the shutter to focus and tell you what the exposure will be, or press the "*" button for an exposure measurement only.
Auto: in auto mode, it only sets the scene once at the start. If you start shooting while your camera is in the bag, or the lens cap is on, then when you bring it out into the light, it will be overexposed.