Based on dynamical modeling, robust trajectory tracking control of a spherical mobile robot is proposed. The spherical robot is composed of a spherical shell and three independent rotors which act as the inner driver mechanism. Owing to rolling without slipping assumption, the robot is subjected to two nonholonomic constraints. The state space representation of the system is developed using dynamical equations of the robot's motion. As the main contribution, a dynamical model based SMC (sliding mode controller) is designed for position control of the robot under parameters uncertainty and unmodeled dynamics. To decrease the chattering phenomena originated by the sign function, the well-known boundary layer technique is imposed on the SMC. The control gains are determined through using Lyapanov's direct method in such a way that the robustness and to zero convergence of the controller's tracking error are guaranteed. Wide range computer simulations are performed to show the significant tracking performance of the proposed SMC in particular against parameters uncertainty and white Gaussian noises. The simulation results show the significant performance of the designed nonlinear control system in trajectory tracking control of the spherical robot even in the presence of parameters uncertainty and unmodeled dynamics.