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For the discontinuous path tracking problem of wheeled mobile robots with given velocity requirement, it was transformed into the trajectory planning and trajectory tracking problems. Firstly, for the given position and velocity requirements, quintic Bezier curve was used to parameterize the trajectory. Then the trajectory planning problem was transformed into the nonlinear optimization problem, for which the energy and interval times were selected as the optimization objective to optimize the parameterized trajectory. By solving the nonlinear optimization problems, a continuous and smooth trajectory was generated, which satisfied the given position and velocity requirements. Secondly, by exploiting the differential flatness properties of the wheeled mobile robots system, a feedforward controller was designed by using the differential-flatness approach. Thirdly, the kinematic model of the wheeled mobile robots was linearized at its equilibrium point of the feedforward control by using the first order Taylor expansion. Then, an linear time-varying error model was deduced. By defining a new error variable, a feedback controller was designed and the stability of closed loop error system was proved in the Lyapunov framework. Therefore, a two degree of freedom trajectory tracking controller was given. This method had the advantages of simple structure and clear engineering significance. In addition, the higher order terms of the Taylor series were considered as a bounded disturbance input, and the robustness of the system was discussed in the framework of input to state stability theory. Finally, the effectiveness of the proposed trajectory planning and trajectory tracking methods was validated on the Pioneer 3-dx wheeled mobile robot experiment platform. It can be seen from the experimental results that the proposed methods can track the discontinuous path with the given velocity requirement precisely.