Back propagation is widely used for deep learning, however, it requires white box cost functions that is formulated and differentiable. It is difficult for non-experts to build the model for the problem for which the effective cost function is not known. In this report, we propose the gradient estimation method with code-division multiplexing that can calculate gradients of weights in the neural network by using multiple forward propagations. The proposed method enables machine learning for the problem with black box cost functions that cannot be formulated but can calculate cost value. In this report, the proposed method is evaluated on the MNIST problem. Evaluation results shows the proposed method can build the model to recognize MNIST digits and the appropriate lengths of spreading code are small in starting phase and large in finishing phase in learning term.