The performance of synchronous reluctance motor (SynRM) control system is reduced as a result of the non-uniform reluctance of the motor as well as magnetic saturation and cross-coupling effect-induced torque ripple. To suppress the torque ripple of SynRM and improve the robustness of SynRM's current control, a composite control strategy based on multi-resonant speed control and the ultra-local model-based deadbeat predictive current control (ULM-DPCC) is proposed. First, multi-resonance control is proposed to suppress torque harmonics. Second, to alleviate the performance degeneration of conventional DPCC caused by inductance mismatch, the robust predictive current control based on ULM is employed, in which the extended state observer (ESO) is used to predict the current and estimate the disturbance. The accurate current tracking can be realized when the motor parameters mismatch occurs, thus improving the anti-interference ability of the system. Furthermore, the torque ripple is well suppressed while the tracking accuracy of the current is guaranteed. Finally, the correctness and effectiveness are confirmed by the simulation and experimental results.