The design problem of the time-delayed controller with the measured acceleration signal is presented, which is used to neutralize the effect of the gro up delay induced by the low-pass filter on active vibration control systems. By means of the reduction method and the state-derivative feedback strategy, a time-delayed velocity-acceleration feedback controller is proposed without the inclusion of the displacement signal, so that the accumulation errors caused by twice integration of the acceleration signal can be avoided. The developed time delayed feedback controller is examined by the computer simulation, with a special focusing on the control performance of a cantilever beam with the piezoelectric actuator and the acceleration sensor. Simulation results demonstrate that the controller can effectively reduce the free vibration response of the intelligent cantilever beam, and compared with the velocity acceleration feedback controller, it has better control effects at different time delays.