Optical waves can be described by intensity and phase. However, optical waves oscillate too fast for detectors to measure anything but time-averaged intensities. This is unfortunate since the phase can reveal important information about the object. Therefore, it is necessary to apply the known intensity information to retrieve the phase information, which is called phase retrieval. As a classical phase retrieval algorithm, the Gerchberg-Saxton iteration method has the characteristics of continuous error reduction, but a large number of iterations are needed to obtain high-quality retrieval results. The field of neural network algorithm was initially inspired by the goal of modeling biological neural systems, but then parted ways and became an engineering problem with good results in the field of machine learning. This kind of network relies on the complexity of the system to process information by adjusting the interconnection among a large number of internal nodes. A new algorithm combined the neural network and the Gerchberg-Saxton iterative is proposed. Firstly, the initial phase is obtained by Gerchberg-Saxton iteration method, and then a good training model is obtained by using paired initial phase and precise phase training neural network. For the samples in the test set, the trained model is applied to the phase retrieval results of Gerchberg-Saxton iteration method to obtain more accurate phase results. Experiments proved that the better retrieval results with a few iterations can be acquired.