Despite the success of convolutional neural network (CNN) in conventional closed-set recognition (CSR), it still lacks robustness for dealing with unknowns (those out of known classes) in open environment. To improve the robustness of CNN in open-set recognition (OSR) and meanwhile maintain its high accuracy in CSR, we propose an alternative deep framework called convolutional prototype network (CPN), which keeps CNN for representation learning but replaces the closed-world assumed softmax with an open-world oriented and human-like prototype model. To equip CPN with discriminative ability for classifying known samples, we design several discriminative losses for training. Moreover, to increase the robustness of CPN for unknowns, we interpret CPN from the perspective of generative model and further propose a generative loss, which is essentially maximizing the log-likelihood of known samples and serves as a latent regularization for discriminative learning. The combination of discriminative and generative losses makes CPN a hybrid model with advantages for both CSR and OSR. Under the designed losses, the CPN is trained end-to-end for learning the convolutional network and prototypes jointly. For application of CPN in OSR, we propose two rejection rules for detecting different types of unknowns. Experiments on several datasets demonstrate the efficiency and effectiveness of CPN for both CSR and OSR tasks.