A kind of phase retrieval algorithm, which combines Zernike-mode decomposition with stochastic parallel gradient descent (SPGD), is raised to realize wavefront phase recovery based on pupil phase diversity (PPD). The performance of phase retrieval algorithm is analyzed through two different aberrated wavefronts. One is an initial shape of 32-element deformable mirror sampled by the interferometer; the other is generated through the method proposed by Roddier. Simulation results show that above two aberrated wavefronts can be restored successfully. For relatively small aberrations, satisfactory results are obtained only using the mode decomposition. When the aberrated wavefronts include many high frequency components, the algorithm only using the mode decomposition does not fit for this situation because of coupling among different orders. The results of the mode decomposition are used as the initial solution of SPGD algorithm, which searches the optimum solution. Simulation results under noise show the phase retrieval algorithm has strong anti-noise ability.