As a major representative nonholonomic system, wheeled mobile robot (WMR) is often used to travel across off-road environments that could be unstructured environments. Slippage often occurs when WMR moves in slopes or uneven terrain, and the slippage generates large accumulated position errors in the vehicle, compared with conventional wheeled mobile robots. An estimation of the wheel slip ratio is essential to improve the accuracy of locomotion control. In this paper, we propose an improved adaptive controller to allow WMR to track the desired trajectory under unknown longitudinal slip, where the stabilisation of the closed-loop tracking system is guaranteed by the Lyapunov theory. All system states use neural network online weight tuning algorithms, which ensure small tracking errors and no loss of stability in robot motion with bounded input signals. We demonstrate superior tracking results using the proposed control method in various Matlab simulations.