An adaptive trajectory tracking problem for a spherical rolling robot driven by a 2DOF pendulum is considered in this paper. A feedback controller is proposed for the goal of tracking the trajectory for the full configuration of the spherical robot. To deal with time-varying uncertainty of the system dynamics, an adaptation mechanism is included in the trajectory tracking controller by parameterizing the system uncertainty with a polynomial function, weighted by unknown constant parameters adjustable by the defined update law. The constructed controller is first tested for the planar hoop-pendulum and then applied to the ball-pendulum system. The convergence to the desired trajectories under the control law is proved and then verified by simulations for tracking circular motions under perturbation.