The GS (Gerchberg-Saxton) algorithm has the disadvantages of slow convergence, low accuracy, and easily falling into local minimum values. The GS algorithm is very sensitive to the initial phase. Usually, the closer the estimated initial phase is to its true value, the better the obtained recovery result is. Therefore, in order to obtain the initial phase more close to its true value, we added a non-redundant aperture mask on the pupil of a telescope, and then we processed the interferogram formed by the mask to obtain the initial phase. This method can effectively improve the convergence speed and running accuracy of the GS algorithm. The efficiency of this algorithm was verified via a computer simulation. The simulation results show that the average recovery accuracy of the proposed algorithm is at least nine times that of the GS algorithm.