Spherical mobile robot is a special non-chained nonholonomic system with underactuation and strong coupling, which make its trajectory tracking control very difficult and complex to realize. Precise trajectory tracking control depends on concise and accurate dynamic model. However, the current researches of trajectory tracking control rarely considered the influence of nonlinear factors and uncertain disturbances of spherical robot. In order to achieve strong robustness and anti-interference of trajectory tracking control of spherical robot, taking spherical mobile robot driven by a two-degrees of freedom pendulum as the research object, its complete dynamic model was established with Boltzmann-Hamel equation and simplified to obtain the one easy to control and with the key motion characteristics. Aiming at the modeling uncertainty of the spherical robot and the environment disturbances that may be encountered during movements, an adaptive sliding mode trajectory tracking control based on double power reaching law was proposed and proved to be stable by Lyapunov theorem. The effectiveness and robustness of the proposed control law are verified through simulations.