Wheel mobile robots have been widely used for applications in industry, military purposes, entertainment and transport. Many factors can affect the performance of the control system such as surface friction, wind, rainfall and time-varying load. Dealing with these uncertain things is challenging and interesting. This article proposes an adaptive tracking control scheme based on a function estimator for three-wheeled mobile robots under the influence of model uncertainty and disturbance. All functions in the dynamic model are combined with disturbances to create a new lumped function of the system. Then, it is estimated by using the Euler formula with an approximate solution. This estimation is used to design a model-based kinetic controller. The stability of the system is analyzed with the Lyapunov stability theory to guarantee the boundedness of the tracking error. Finally, numerical simulations and comparison results with the existing adaptive controller are taken to verify the effectiveness of the proposed method.