1. An image pickup apparatus that outputs picked-up images on a frame-by-frame basis from an image pickup element having a plurality of pixels, the image pickup apparatus comprising: a shutter-speed setting unit configured to set a shutter speed for still-image pickup; a frame-rate setting unit configured to set an image-pickup frame rate based on the shutter speed set by the shutter-speed setting unit; a control unit configured to control an operation of the image pickup element such that the picked-up images are output at the image-pickup frame rate; and a moving-image reproducing unit configured to perform moving-image reproduction by using the picked-up images, wherein, when the image-pickup frame rate set by the frame-rate setting unit is higher than a moving-image-reproduction frame rate, the moving-image reproducing unit generates a frame for use in the moving-image reproduction from a plurality of frames of the picked-up images and performs reproduction at the moving-image-reproduction frame rate.