Trajectory reconstruction aims to recover the missing position of moving objects in a given video, which is important for predicting the behavior of motion objects. The existing trajectory estimations focus on frame-by-frame object detection and tracking. However, these methods cannot handle complex situations such as mutual occlusion of multiple objects. To solve the posed problem, we propose a novel motion trajectory reconstruction based on object matching and graph signal processing. Specifically, we first extract the features of objects by detection and then perform object matching via similarity scores. The gradient graph Laplacian regularizer is used to interpolate the missing trajectory signals. We can effectively reconstruct motion trajectory signals with a higher sampling ratio of video frames. We do not require knowledge of the underlying motion information and can accurately estimate the position in occlusion. Experimental results show that the quality of our trajectory reconstruction outperforms other competing algorithms.