With the advent of neural network, unprecedented advancements have been achieved in many tasks, including radar signal processing. However, a key disadvantage of the current methods is the black-box structure, which makes it hard to interpret or assess the hidden representations of data. In this paper, by combining the physical generative mechanism of the high range resolution (HRR) radar signal with neural network, we develop an interpretable deep probabilistic model to learn the latent features from HRR radar signals that can characterize the physical structure of targets. In detail, based on the radar target's scattering center model which describes the HRR radar signal as the summation of echoes from the scattering centers, a deep probabilistic model is constructed to depict the generative process from the scattering centers to observations, where the latent features comprise the locations and amplitudes of scattering centers. Considering that the locations of scattering centers are nearly invariable and the amplitudes of them are fluctuant for the signals within a small angular range, our model defines the shared locations and independent amplitudes of scattering centers for the signals in a small angular range, aiming to improve the robustness of interpretable feature extraction model. In addition, our model performs probabilistic inference on the posterior distribution of latent features with high preciseness. With the proposed model, we further design a recognition scheme based on the minimum reconstruction error criterion. Experiments on the measured HRR radar dataset validate the effectiveness of our model on learning interpretable features and superior recognition performance.