This paper introduces two algorithms of the phase retrieval——Gerchberg-Saxton algorithm and gradient search algorithm.We respectively get the objective function of gradient search algorithm about the generalized pupil,wave-front and the Zernike coefficients of the partial derivatives when multi-frame images and their defocus are used as the inputs.The relationship between GS algorithm and the gradient search algorithm is revealed.Simulation experiments are carried out with GS algorithm and gradient search algorithm when single and multiple images are used as inputs.The experiment results show that the gradient search algorithm is superior to GS algorithm for single image input.Both GS algorithm and gradient search algorithm can work out wave-front for multi-frame images with different defocus as the input,but the convergence speed of gradient search algorithm is evidently better than GS algorithm.