Various palmprint recognition methods have been proposed and applied in security, particularly authentication. However, improving the performance of palmprint recognition with insufficient training samples per person is still a challenging task. The undersampling problem limits the application and popularization of palmprint recognition. In this article, by regularly sampling different local regions of the palmprint image, we learn complete and discriminative convolution features by using deep convolutional neural networks (DCNNs). With this powerful palmprint description, a joint constrained least-square regression (JCLSR) framework, which performs representation for each local region of the same palmprint image requiring all regular local regions of the palmprint image to have similar projected target matrices, is presented to exploit the commonality of different patches. The proposed method can well solve the undersampling classification problem in palmprint recognition. Experiments were conducted on the IITD, CASIA, noisy IITD, and PolyU multispectral palmprint databases. It can be seen from the experimental results that the proposed JCLSR consistently outperformed the classical palmprint recognition methods and some subspace learning-based methods for palmprint recognition.