An image stabilizing apparatus and an image pickup apparatus that can detect shift shake reliably with a simple configuration and make highly accurate image blur correction possible even at very short subject distances. The apparatus has an angular velocity detector for detecting the angular velocity generated by shaking of the apparatus, an acceleration detector for detecting acceleration generated by the shaking, tor for calculating a correction value from the angular velocity, an acceleration corrector for correcting the acceleration based on the shake correction value, and a blur corrector for correcting image blur by decentering an optical axis based on an output of the acceleration corrector and an output of the calculator.