Traditional domain adaptation (DA) research generally assume that the source and target domains have the same label set. However, in many real-world applications, there exists a more general and practical situation where target label set is just a subset of  source label set, which is formulated as partial domain adaptation (PDA) problem. Compared with DA, PDA is more vulnerable to negative transfer due to the mismatch of label sets. In this paper, we propose a novel PDA method {based on Progressive sample Learning of Shared Classes (PLSC)}, which contains two main parts: shared classes identification and progressive target sample learning. The shared classes identification component aims to exclude source-private classes and merely allow source samples within shared classes to participate in the progress of knowledge transfer. To achieve this goal,  following the separation and alignment assumptions in DA, we minimize the sum of the distances from both source and target samples to their corresponding source class centers, and then design an adaptive threshold to determine the shared classes. Furthermore, considering the misleading  of  target samples that deviate from the source class centers, we propose to progressively include target samples for subspace learning by introducing self-paced learning mechanism. Extensive experiments verify the superiority of our method against the existing counterparts.