We present a secure backpropagation neural network training model (SecureBP), which allows a neural network to be trained while retaining the confidentiality of the training data, based on the homomorphic encryption scheme. We make two contributions. The first one is to introduce a method to find a more accurate and numerically stable polynomial approximation of functions in a certain interval. The second one is to find a strategy of refreshing ciphertext during training, which keeps the order of magnitude of noise at O˜e33.