Model-free predictive control directly computes the control input from massive input/output datasets and does not use a mathematical model. In contrast, conventional model predictive control relies on mathematical models. Although the underlying principle of model-free predictive control utilizes linear regression vectors comprising input/output data, it can also be applied to control nonlinear systems. In this study, the linear regression vectors are extended to polynomial regression vectors, improving the control performance. Using numerical simulations, we demonstrate the effectiveness of this approach.