In this paper a controller has been presented based on the predictive control to drive and control the bipedal Nao robot. One of the challenges in the practical applying of these types of controllers is their high computational loading and the time-consuming control operations in each time step, in which it is suggested to use Laguerre Functions to reduce the computational loading of the predictive controller. In this study, at first using the conventional methods for the identification, and via the real data obtained from the Nao robot in Mechatronics research center of Qazvin Azad University, a proper model is proposed for walking the Nao robot which is considered as a two-dimensional motion in the plane. Then a controller will be designed to control the robot motion using the model based predictive controller. The purpose of this control approach in the first place is to stabilize the walking of the robot and then to guide and keep it on the desired trajectory, so that this trajectory tracking can be performed well as much as possible. Moreover, in order to evaluate the efficiency of the proposed controller, this controller has been compared with a proportional-integral-derivative controller and will be studied. The simulation results show the effectiveness of the proposed controller performance in the robot trajectory tracking, which finally comparing the obtained results from both of the control approaches, indicates the efficiency and different capabilities of the proposed method in this study.