In this paper, we propose a deep shape descriptor by learning the shape distributions at different diffusion time via a progressive deep shape-distribution-encoder. First, we develop a shape distribution representation with the kernel density estimator to characterize the intrinsic geometrical structure of the shape. Then, we propose to learn discriminative shape features through a progressive shapedistribution-encoder. Specially, the progressive shape-distributionencoder aims at modeling the complex non-linear transform of the estimated shape distributions between consecutive diffusion time. Furthermore, in order to characterize the intrinsic structure of the shape more efficiently, we stack multiple proposed progressive shapedistribution-encoders to form a neural network structure. Finally, we concatenated all neurons in the hidden layers of the progressive shape-distribution-encoder network to form a discriminative shape descriptor for retrieval. The proposed method is evaluated on three benchmark 3D shape datasets and the experimental results demonstrate the superiority of our method to the existing approaches.