The origin-destination pair of vehicles was introduced into the Biham-MiddletonLevine (BML) model with four-directional traffic to investigate the dynamical evolution process of urban traffic flow under a periodic boundary. The driver selects the shortest path to their destination considering not only the relative position but also the parity of rows (columns). When a static route choice strategy is used, local gridlocks occur at very low density because the path is already determined at the initial moment, and it is ineffective to improve the critical density. Using the dynamic route choice strategy based on global traffic information, the driver can change the direction of motion to avoid congested areas when the steering condition is satisfied according to the speed threshold. Simulation results show that using a smaller threshold value can effectively reduce traffic congestion without significantly increasing travel distance. The fluctuations of mean speed can be further reduced if a local control strategy in a subdomain is adopted.