Conventional Model predictive control (MPC) techniques in motor drives typically rely on the necessity of an a priori known accurate plant model. However, the strong time-varying effect of motor parameters with parasitic effect may significantly affect the MPC performance. The least-squares (LS) algorithm has been introduced to motor drives to avoid the dependence on accurate models for MPC. However, such a strategy could be unreliable in the presence of noisy measurements. To address this issue, this article proposes a robustness-improved data-driven predictive current control method utilizing iteratively reweighted least squares (IRLS) solution for permanent magnet synchronous motor (PMSM) drives. The proposed method effectively avoids the influence of system noise on the performance of the LS model by online weighting of measurement data based on current prediction residuals. It does not require any offline training or parameter configurations with exceptional generalization ability. Experimental validation on a PMSM test bench demonstrates superior robustness and satisfactory control performance, especially during transient and steady-state operations, compared to the conventional LS approaches.