In this paper, a novel perceptual image hashing scheme based on convolutional neural network (CNN) with multiple constraints is proposed, in which our deep hashing network learns the process of features extraction automatically according to the training target and then generates the final hash sequence. The combination of convolutional and pooling layers is to reduce the size of input image while deepening the channels. Then, we construct two pairs of constraints and integrate them into an overall constraint function through a strategy of weight allocation. In order to guarantee the robustness and discrimination of deep hashing network simultaneously, a new training method is developed to adjust the training set structure dynamically according to the changes of constraint values. Experimental results show that the proposed deep hashing network can achieve a satisfactory balance between perceptual robustnzess and discrimination while maintaining security. Based on the large-scale test set, receiver operating characteristic (ROC) curves, ${F}_{1}$ scores and equal error rate (EER) demonstrate the superiority of our scheme in terms of content authentication compared with some state-of-the-art schemes.