In order to reinforce the operation stability and obstacle capability of a spherical robot, this paper presents a spherical robot with high-speed rotating flywheel, the mechanical structure of which is mainly composed of a spherical shell, a double pendulum on both sides and two high-speed flywheels. The robot has three excitation modes: level running, self-stability operating, and obstacle surmounting. The dynamic characteristics of the pendulum, flywheel, and brake of the robot are discussed through the establishment of kinematic and dynamic model of the spherical robot and the influence of parameters like weight, flywheel speed. and flywheel position on its dynamic characteristics and robot performance is optimized and analyzed in detail. The research results indicate that the two flywheels located in the center of the sphere apart can bring maximum stability gain to the sphere. Finally, the simulation and experiment of the stability gain brought by the high-speed flywheel to the sphere verify that the operation stability of the sphere is effectively improved after using the flywheel, and the robot that stops the flywheel through a brake fixed on the pendulum has better obstacle surmounting performance.