This paper address the problem of control an underactuated two-wheel robot to follow a desired tracking path under unknown road disturbance. Based on the robot practical kinematics and dynamics model, the unknown road damping force should be nonlinear and related with wheels' velocity. The solutions include a Lyapunov-based trajectory tracking control law and disturbance estimator. In mathematics aspect, the control algorithm is solving the position, orientation and velocity error's boundedness and convergence problem. In general, all errors should be approaching to equilibrium states. According to real robot model, the controller performance includes following aspects: i) working against unknown road disturbance, i) considering the saturation problem of position error, iii) computing the nonlinear pa-rameters in robot model. Finally, in order to validate the controller, an experiment system was desined which is based on Matlab software on host computer and Inverted Pendulum Two-Wheeled Robot with Arduino MCU (Microprogrammed Control Unit) and DC (Direct Current) motor as lower computer. © 2018 IEEE.