This study proposes a semi-active on-off damping controller that is a mix of three conventional ground-hook controllers for semi-active tuned mass damper systems. Three conventional ground-hook controllers are shown to be effective only in a certain frequency range. By taking advantage of all three ground-hook controllers, the mixed controller shows its better performance. More-over, we found an analytical solution of the harmonic vibration of the semi-active controlled system. The accuracy of the analytical solution and the superior performance of the proposed controller are verified by the numerical simulations.