Active vibration control of automotive drivetrains must be developed to compensate for the backlash of gears because it causes undesired responses. In addition, an engine used as an actuator has a constraint which makes the control periods longer and time-varying, resulting in deterioration of the control performance. The contribution of this study is to cope with all the issues described above, backlash and the control period constraint, simultaneously. First, a basic experimental device, which simplifies an actual vehicle to focus on the effect due to backlash, is demonstrated. In the device, the control period constraint, which is equivalent to that of an engine, is reproduced by a digital signal processor. To reduce an adverse effect due to the extension of the control period, the sampled-data controller, which does not require discretization in its implementation, is employed. In this paper, predictive processing using the servo-type sampled-data controller is proposed to compensate for the phase delay of the control input caused by the time-varying control period. In addition, a control mode switching technique included in the prediction suppresses undesired responses due to backlash. Finally, control experiments verify the effectiveness of the control system.