1. An image pickup apparatus comprising: an image pickup element operable to capture a plurality of still images at a shutter speed to obtain captured images; an auto exposure unit operable to calculate a calculated shutter speed; a detection unit operable to detect a power supply frequency if the calculated shutter speed is longer or equal to a predetermined value; a setting unit operable to set the shutter speed to a value equal to N/(2f), where N is an integer and f is the power supply frequency detected by the detection unit, and shorter than the calculated shutter speed in response to a predetermined user operation, if the calculated shutter speed is longer than or equal to a predetermined value; and a storage unit operable to store: an upper limit of the shutter speed, an upper limit of an analog gain, and a hand shake threshold value, wherein the setting unit is further operable to calculate the analog gain to increase a brightness of the captured images to compensate for a decrease in brightness of the captured images due to a shortening of the shutter speed and the setting unit is further operable to calculate a candidate analog gain for each shutter speed that is equal to an integral multiple of 1/(2f) and is shorter than or equal to the upper limit of the shutter speed; and select a candidate shutter speed for which the candidate analog gain does not exceed the upper limit of the analog gain to obtain a selected shutter speed.