This work investigates the problem of fixed-time trajectory tracking control for a nonholonomic wheeled mobile robot(WMR) under the external disturbance. The novel integral sliding mode surface(ISMS) based fixed-time kinematic velocity controllers are first designed for the kinematic error model of the WMR, which can guarantee the tracking errors converge to the small neighborhoods of origin in a fixed time. Subsequently, a continuous fixed-time disturbance observer is developed to estimate the external disturbance for the dynamic model of the WMR. Then, a trajectory tracking controller is designed based on the ISMS to ensure the fixed-time stability of the dynamic system, which achieves the high precision trajectory tracking control of the WMR. Finally, the simulation results illustrate the effectiveness and superiority of the proposed approach.