The Mecanum-wheeled robot has four special wheels. It can control four wheels independently and has seven turning axes. The robot can translate in all directions and travel in curves without changing its direction by means of the control commands for turning ratio, speed, and direction of travel. However, no model has been proposed that can accurately simulate the output of the actual machine for the three types of inputs, even when the characteristics of the motor and motor driver are unknown. In this study, we synthesized and simplified transfer functions and estimated the undetermined coefficients that minimize the sum of squared errors to construct a model of the robot that can output the position and posture equivalent to those of the actual robot for the input commands for turning ratio, speed, and the direction of travel. We modeled a Mecanum-wheeled robot using the proposed modeling method and parameter determination method and compared the outputs of the real robot to the step and ramp inputs. The results showed that the errors between the two outputs were very small and accurate enough to simulate AI learning, such as reinforcement learning, using the model of the robot.