Since there are complex geometric variations with 3D shapes, extracting efficient 3D shape features is one of the most challenging tasks in shape matching and retrieval. In this paper, we propose a deep shape descriptor by learning shape distributions at different diffusion time via a progressive shape-distribution-encoder (PSDE). First, we develop a shape distribution representation with the kernel density estimator to characterize the intrinsic geometry structures of 3D shapes. Then, we propose to learn a deep shape feature through an unsupervised PSDE. Specially, the unsupervised PSDE aims at modeling the complex non-linear transform of the estimated shape distributions between consecutive diffusion time. In order to characterize the intrinsic structures of 3D shapes more efficiently, we stack multiple PSDEs to form a network structure. Finally, we concatenate all neurons in the middle hidden layers of the unsupervised PSDE network to form an unsupervised shape descriptor for retrieval. Furthermore, by imposing an additional constraint on the outputs of all hidden layers, we propose a supervised PSDE to form a supervised shape descriptor, where for each hidden layer the similarity between a pair of outputs from the same class is as small as possible and the similarity between a pair of outputs from different classes is as large as possible. The proposed method is evaluated on three benchmark 3D shape datasets with large geometric variations, i.e., McGill, SHREC’10 ShapeGoogle and SHREC’14 Human datasets, and the experimental results demonstrate the superiority of the proposed method to the existing approaches.