We propose a new phase retrieval algorithm based on the combination of the Monge-Ampère equation and the iterative angular spectrum algorithm. Since the iterative angular spectrum algorithm is highly dependent on the initial value, we utilize the solution of the Monge-Ampère equation to initialize it, which is expected to yield more accurate results than the solution of the transport of intensity equation. To avoid the algorithm becoming stuck in local minima and iteration stagnation, we adopt an alternating iteration strategy between the traditional iterative angular spectrum algorithm and hybrid input-output algorithm. The effectiveness of the hybrid algorithm is demonstrated by numerical experiments.