The license plate data captured by a traffic information collection device is a natural carrier for studying the trajectory of a vehicle and is useful to track and restore the complete trajectory of the vehicle on the road network. However, due to the limitations of technology and device coverage, the collected time series data of license plates is inevitably sparse and incomplete. To make full use of license plate data, this study proposes an origin-destination (OD) trajectory restoration algorithm based on sparse license plate data. The algorithm first separates the OD trip chain of the vehicle by the interval time threshold. Then, it generates multiple approximate candidate trajectories with the K-shortest path (KSP) algorithm. Finally, a variational autoencoder (VAE) is used to select the optimal estimated trajectory for decision-making so that the complete trajectory of the vehicle can be obtained. This method has been implemented and verified in an actual transportation analysis zone in Xiaoshan District, Hangzhou City. The results show that the proposed method achieves a comprehensive accuracy of 95%. Additionally, the reconstruction method still has sound performance (higher than 50%) in the case of a high node loss rate and low camera coverage.