The global navigation satellite system (GNSS) and inertial navigation system (INS) integrated navigation system have been widely used in Intelligent Transportation Systems (ITSs). However, the positioning error of integrated navigation systems is rapidly divergent when GNSS outages occur. Motion constraint and back propagation (BP) neural networks can provide additional knowledge to solve this issue. However, the predictions of a neural network have outliers and motion constraint is difficult to adapt according to the motion states of vehicles and boats. Therefore, this paper fused a BP neural network with motion constraints, and proposed a motion-constrained GNSS/INS integrated navigation method based on a BP neural network (MC-BP method). The pseudo-measurement of the GNSS was predicted using a fitting model trained by the BP neural network. At the same time, the prediction outliers were detected and corrected using motion constraint. To assess the performance of the proposed method, simulated and real data experiments were conducted with a vehicle on land and a boat offshore. A classical GNSS/INS integration algorithm, a motion-constrained GNSS/INS algorithm, and the proposed method were compared through data processing. Compared with the classical GNSS/INS integration algorithm and the motion-constrained GNSS/INS algorithm, the positioning accuracies of the proposed method were improved by 90% and 64%, respectively, in the vehicle land experiment. Similar performances were found in the offshore boat experiment. Using the proposed MC-BP method, improved meter-level-positioning results can be achieved with the GNSS/INS integration algorithm when GNSS outages occur.