In order to maintain a stable spin and high-speed rotation of superconducting spherical rotors at low temperatures, a spin drive device for superconducting rotors is designed based on the Meissner effect. The spin drive device includes a superconducting stator and a superconducting spherical rotor. The stator is fitted two-phase coils and the rotor is a hollow structure with four windows in its inner wall. The electromagnetic field generated by the stator coils can produce a rotating torque on the windows in the inner wall to drive the rotor to rotate. Then,the driving force is calculated using the Ansoft software, and analysis results show that the driving torque is approximately in proportional to the square of drive current. Rotation experiments are performed at 4.2 K, 30 Pa and rotation speed is up to 8 512 r/min in a drive current of 30 A. Experimental results indicate that the drive device can accelerate the rotor to an operating speed above 8 500 r/min, which provides valuable references for the further improvement of the design parameters of drive devices and the rotation stability of superconducting spherical rotors.