This paper proposes a new method, i.e., weighted hierarchical depth motion maps (WHDMM) + three-channel deep convolutional neural networks (3ConvNets), for human action recognition from depth maps on small training datasets. Three strategies are developed to leverage the capability of ConvNets in mining discriminative features for recognition. First, different viewpoints are mimicked by rotating the 3-D points of the captured depth maps. This not only synthesizes more data, but also makes the trained ConvNets view-tolerant. Second, WHDMMs at several temporal scales are constructed to encode the spatiotemporal motion patterns of actions into 2-D spatial structures. The 2-D spatial structures are further enhanced for recognition by converting the WHDMMs into pseudocolor images. Finally, the three ConvNets are initialized with the models obtained from ImageNet and fine-tuned independently on the color-coded WHDMMs constructed in three orthogonal planes. The proposed algorithm was evaluated on the MSRAction3D, MSRAction3DExt, UTKinect-Action, and MSRDailyActivity3D datasets using cross-subject protocols. In addition, the method was evaluated on the large dataset constructed from the above datasets. The proposed method achieved 2-9% better results on most of the individual datasets. Furthermore, the proposed method maintained its performance on the large dataset, whereas the performance of existing methods decreased with the increased number of actions.