With the development of aerospace technology, more and more scientific activities are carried out in the universe. Due to the microgravity environment of space, the control of the 6-DOF platform is different from those on the earth. First, a virtual prototype model of the 6-DOF non-contact platform was built in ADAMS. The dynamics model was developed based on the Newton–Euler method. Then, the 6-DOF backstepping sliding mode controller and disturbance observer were designed in MATLAB/Simulink. Finally, by combining the virtual prototype model in ADAMS and the control system in MATLAB, the co-simulation model was proposed. According to the simulation results, the 6-DOF backstepping sliding mode controller can well complete the positioning, 3D trajectory tracking, and vibration isolation tasks of non-contact 6-DOF platform. Quantitatively, the spatial error of backstepping sliding mode controller’s 3D trajectory tracking is only 50% of the ordinary sliding mode control and it is 20% of the nonlinear propotional-derivative-integral.