Complex-valued Associative Memory (CAM) is an advanced model of Hopfield Associative Memory. The CAM is based on multi-state neurons and has the high ability of representation. Lee proposed gradient descent learning for the CAM to improve the storage capacity. It is based on only the phases of input signals. In this paper, we propose another type of gradient descent learning based on both the phases and the amplitude. The proposed learning method improves the noise robustness and accelerates the learning speed.