1. An image pickup apparatus having a function of detecting image shaking, comprising: a first image shaking detection unit which detects image shaking based on a size of a motion vector which represents a movement amount of each pixel and is detected from a plurality of successively obtained image frames; a second image shaking detection unit which calculates a difference value obtained by comparing respective pixel values of pixels located at identical positions in a plurality of successively obtained image frames, to detect image shaking; and a determination unit which determines whether image shaking detected by the first image shaking detection unit has converged by comparing the motion vector with a first threshold, and which determines whether image shaking detected by the second image shaking detection unit has converged by comparing the difference value with a second threshold; wherein the determination unit determines that image shaking has disappeared, when, after image shaking detected by the first image shaking detection unit is determined to have converged, image shaking detected by the second image shaking detection unit is further determined to have converged; and wherein the determination unit does not determine that image shaking has disappeared before image shaking detected by the first image shaking detection unit is determined to have converged, even if image shaking detected by the second image shaking detection unit is determined to have converged.