The Dynamic Vehicle Routing Problem (DVRP) is an extension of the Vehicle Routing Problem (VRP), which gains its complexity from the dynamic nature of demand. Current methodologies are constrained by a single problem space, which may lead to unsatisfactory solutions in the face of dynamic situations. Therefore, a novel multi-space evolutionary search algorithm (NMSES) is proposed in this paper to solve DVRP, which considers the time windows. Specifically, for a given DVRP, it is divided into several static VRPs for solving. For each VRP, the original data domain is defined as the original problem space, and the simplified problem space is established by a clustering method to assist the evolutionary search. In the dynamic context, the simplified problem space is quickly re-established with the historical optimal solution. Subsequently, evolutionary searches in both spaces occur independently. A knowledge transfer strategy is applied to transfer the knowledge of the simplified problem space to the original problem space, which optimize the algorithm’s performance. The empirical studies are conducted on the widely recognized Homberger benchmark to verify the effectiveness of the NMSES.