An image pickup apparatus that is capable of reducing the load of the process required to combine images with different exposures to generate a composite image. An image pickup unit performs continuous image pickup that shoots a subject continuously under different exposure conditions. A control unit controls the image pickup unit so that the exposure condition for the first shot in a current set, which is a second or later set, is coincident with the exposure condition for the last shot in the previous set when a plurality of sets of the continuous image pickup are performed. A composing unit composes the images acquired by one set of the continuous image pickup by the image pickup unit to generate one output image.