We propose an efficient training method for memristor neural networks. The proposed method is suitable for the mini-batch-based training, which is a common technique for various neural networks. By integrating the two processes of gradient calculation in the backpropagation algorithm and weight update in the write operation to the memristors, the proposed method accelerates the training process and also eliminates the external computing resources required in the existing method, such as multipliers and memories. Through numerical experiments, we demonstrated that the proposed method achieves twice faster convergence of the training process than the existing method, while retaining the same level of the accuracy for the classification results.