For 3D shape analysis, an effective and efficient feature is the key to popularize its applications in 3D domain. In this paper, we present a novel framework to learn and extract local deep feature (LDF), which encodes multiple low-level descriptors and provides high-discriminative representation of local region on 3D shape. The framework consists of four main steps. First, several basic descriptors are calculated and encapsulated to generate geometric bag-of-words in order to make full use of the various basic descriptors' properties. Then 3D mesh is down-sampled to hundreds of feature points for accelerating the model learning. Next, in order to preserve the local geometric information and establish the relationships among points in a local area, the geometric bag-of-words are encoded into local geodesic-aware bag-of-features (LGA-BoF). However, the resulting feature is redundant, which leads to low discriminative and efficiency. Therefore, in the final step, we use deep belief networks (DBNs) to learn a model, and use it to generate the LDF, which is high-discriminative and effective for 3D shape applications. 3D shape correspondence and symmetry detection experiments compared with related feature descriptors are carried out on several datasets and shape recognition is also conducted, validating the proposed local deep feature learning framework.