For many real-world multimedia applications, data are often described by multiple views. Therefore, multi-view learning researches are of great significance. Traditional multi-view clustering methods assume that each view has complete data. However, missing data or partial data are more common in real tasks, which results in partial multi-view learning. Therefore, we propose a novel multi-view clustering method, called Partial Multi-view Subspace Clustering (PMSC), to address the partial multi-view problem. Unlike most existing partial multi-view clustering methods that only learn a new representation of the original data, our method seeks the latent space and performs data reconstruction simultaneously to learn the subspace representation. The learned subspace representation can reveal the underlying subspace structure embedded in original data, leading to a more comprehensive data description. In addition, we enforce the subspace representation to be non-negative, yielding an intuitive weight interpretation among different data. The proposed method can be optimized by the Augmented Lagrange Multiplier (ALM) algorithm. Experiments on one synthetic dataset and four benchmark datasets validate the effectiveness of PMSC under the partial multi-view scenario.