To improve the quality of starting torque and suspension force, a composite cage rotor bearingless induction motor (CCR-BIM) is designed, which adopts a composite cage rotor structure that combines an inner rotor and an outer rotor. First, the overall structure of the CCR-BIM is designed, the composite cage rotor of the CCR-BIM is specially designed and analyzed for the induction principle, and the mathematical model of suspension force and torque is deduced. Second, the initial structural parameters are determined, and motor qualities, such as starting torque quality and suspension force quality, are compared and analyzed between the proposed motor and BIM using a finite element model (FEM). Third, based on the response surface model (RSM), a multi-objective improved NSGA-II is constructed, and the three optimization objectives of starting torque, suspension force, and suspension force pulsation are optimized. Finally, the results of the experimental setup prove that the starting torque increases by 6.98%, the suspension force increases by 5.45%, and the suspension force pulsation decreases by 18.54%. The effectiveness of the proposed motor and the correctness of the multi-objective optimization strategy are verified.