Shape descriptor is a concise yet informative representation that provides a 3D object with an identification as a member of some category. We have developed a concise deep shape descriptor to address challenging issues from ever-growing 3D datasets in areas as diverse as engineering, medicine, and biology. Specifically, in this paper, we developed novel techniques to extract concise but geometrically informative shape descriptor and new methods of defining Eigen-shape descriptor and Fisher-shape descriptor to guide the training of a deep neural network. Our deep shape descriptor tends to maximize the inter-class margin while minimize the intra-class variance. Our new shape descriptor addresses the challenges posed by the high complexity of 3D model and data representation, and the structural variations and noise present in 3D models. Experimental results on 3D shape retrieval demonstrate the superior performance of deep shape descriptor over other state-of-the-art techniques in handling noise, incompleteness and structural variations.