Abstract: A predefined-time consensus control approach is investigated for the leader-following consensus problem of wheeled mobile robot (WMR). First, under the directed graph, a distributed observer is proposed for each follower to estimate the leader's state in a predefined time. Second, on the basis of the observer and a constructed double power reaching law and a nonlinear manifold, a new controller is designed to track the estimated leader state in a predefined time. Moreover, a switching protocol and a linear manifold are referenced to ensure that the controller can achieve leader-following consensus for a predefined time under any initial condition without causing singularity problems. The predefined time stability of the system is then proved by algebraic graph theory and Lyapunov theory. Finally, simulation comparison experiments verify the proposed algorithm's effectiveness and superiority. Compared with that of the finite-time controller, the convergence time of the proposed controller is independent of the initial conditions and the convergence effect is better. Compared with that of the fixed-time controller the convergence time setting of the proposed controller is simpler and a single parameter can directly preset the system convergence time.