In order to solve the problem of the low direct control accuracy of permanent magnet assisted bearingless synchronous reluctance motor (PMa-BSynRM), which caused by transmission delay, the predictive control is applied to direct control of PMa-BSynRM. Meanwhile, in view of the disadvantages of large ripple (torque ripple, flux linkage ripple) and poor robustness in traditional predictive direct control (PDC), a fractional super twisting sliding mode controller (FSTMC) is proposed. Firstly, the mathematical models of torque and radial suspension force of PMa-BSynRM are derived. Secondly, the torque and flux controller based on FSTMC are designed, and the stability is verified. Thirdly, the torque predictive controller and levitation force predictive controller are designed, and the algorithm of PDC is described. Finally, the FSTMC-PDC system of PMa-BSynRM is built and simulated by Matlab/Simulink module. The simulated and experimental results confirm the validity and superiority of the proposed method.