In this paper, an active vibration control method for nonlinear mechanical systems is presented. The control forces are determined by the future values obtained by a short-term prediction method based on chaos theory and the authors call such a control method a predictive control method. The predictive control method is applied to a system for a pendulum forced by a sinusoidal torque at the supported point. The equation of motion for the pendulum becomes nonlinear when the swing angle is large. It is also known that chaotic behaviors occur in such a nonlinear pendulum model under some conditions. Here, a predictive control method to get the control forces using the angular displacements near future is discussed. In addition, a method is presented to find the optimum sampling period to take samples from the response which is continuous with respect to time. The ideas of forward and backward horizons, defined by the authors before, are also taken to the nonlinear pendulum system, and the effectiveness of the control method is examined numerically.