This paper investigates the feedback stabilization problem for a class of discontinuous systems which is characterized by Filippov differential inclusion. Lyapunov-based backstepping design method is generalized with nons-mooth Lyapunov functions to solve the control problem. A set-valued time derivative is introduced first for nonsmooth function along discontinuous vector fields, which enables us to perform Lyapunov-based design with nondifferentiable Lyapunov function. Conditions for designing a virtual control law which is shown nondifferentiable in general in the recursive design problem are proposed. Finally, as a special case, piecewise linear system is discussed to demonstrate the application of the presented design approach. This paper investigates the feedback stabilization problem for a class of discontinuous systems which is characterized by Filippov differential inclusion. Lyapunov-based backstepping design method is generalized with nons-mooth Lyapunov functions to solve the control problem. A set-valued time derivative is introduced first for nonsmooth function along discontinuous vector fields, which enables us to perform Lyapunov-based design with nondifferentiable Lyapunov function. It is shown as nondifferentiable in general that the recursive design problem is proposed. Finally, as a special case, piecewise linear system is discussed to demonstrate the application of the presented design approach.