Configuring an output LC filter for permanent-magnet synchronous motor (PMSM) drives can mitigate the overvoltage issues in long-distance transmission applications. However, the resulting LC-filtered PMSM system may cause an undesired resonance phenomenon, threatening the system's stability. This article proposes a modulated predictive stator current control scheme with capacitor-voltage-feedforward active damping (MPSCC-CVF) to stabilize the LC-filtered PMSM drives. First, a recursion-based stator-current predictive model is established, reducing the computational complexity. Then, a modulated predictive stator current controller with a fixed switching frequency is proposed, which can achieve low current ripples and harmonics. To address the resonance issues, a capacitor-voltage-feedforward active damping strategy is integrated into the proposed MPSCC. Furthermore, the closed-loop stability analysis and parameter tuning are provided in theory. Experimental results validate the feasibility of the proposed scheme.