A double cantilever vibration system with a clearance has the typical non-smooth and nonlinear characteristics, which can induce bifurcation and chaos. Thus, the open-loop control strategy based on energy was studied and a bounded controller was proposed. The chaotic motion of the system can be directed into the stable objective period motion by this strategy. Furthermore, the convergence speed of the controller was analyzed. By numerical simulation, the effectiveness and applicability of this method was demonstrated, which are helpful for designing, vibration control and safety operating of vibro-impact systems.