LC-filtered permanent magnet synchronous motor (LC-PMSM) system is suitable for long-cable drives but it has inherent resonant stability issues. This article presents a modulated model predictive current controller with active damping (AD-M2PCC) for stabilizing the LC-PMSM drive system. First, to avoid the complex exponentiation operations in typical model predictive current control (MPCC), a simplified reduced-order predictive model is constructed and a baseline MPCC is derived based on inverter-side current reference tracking, reducing the computational burden and enhancing the robustness to the model mismatches. Then, a capacitor-current-feedback active damping (AD) is integrated into MPCC for resonance suppression. It has an intuitive damping concept and only one design parameter, significantly lessening the tuning effort. Further, a low-complexity AD-M2PCC scheme is established, which features simple implementation, improved steady-state performance and effective resonance damping. Comparative experimental results are provided to verify the feasibility of the proposed control scheme.