<p>Time-varying piecewise smooth data recovery problem exists extensively in computer vision, image processing, environment monitoring, etc. In recent years, the emerging field of graph signal processing (GSP) provides a new way to solve this problem, deriving the graph signal matrix completion (GSMC) which incorporates the correlation among data entries. The model-based methods of GSMC are more interpretable, but their reconstruction quality is still not satisfactory, especially when observations are sparse. In this paper, we propose a new matrix completion method to solve the time-varying data recovery problem. By jointly exploiting the graph difference operator and the time difference operator to capture the spatio-temporal correlation of the data, we obtain a method based on low-rank and piecewise-differential smoothness (LRPDS). The proposed method achieves high recovery accuracy by jointly exploiting low rank property, the piece- wise smoothness and differential smoothness of graph signals. Numerical results on three real-world datasets demonstrate that our scheme has better reconstruction performance compared with existing model-based matrix completion approaches.</p>