Conventional current control (CC) has been utilized to control the converter's voltage in a wind energy conversion system (WECS) due to its ease of implementation. However, mismatched machine parameters and slow-dynamic response can reduce total system performance. To deal with this issue, this study proposes a robust sliding mode approach-based CC scheme for machine side converter and grid side converter of a grid-connected permanent magnet vernier generator (PMVG). To do this, a direct-drive grid-connected PMVG-based WECS is firstly modeled using a back-to-back converters. Currently, the voltage control references to the converters have been designed using a proportional-integral (PI)-type sliding surface with a modified version of the improved reaching law-based on sliding mode control (SMC) theory. As a result, smooth $dq$-axes voltage references are obtained, which leads to a better steady-state and transient performance from the overall system. Further, the reduced chattering achieves an improved total harmonic distortion reduction in grid current, significantly enhancing the power quality. Then, the Lyapunov stability is derived to verify the reachability condition for the proposed scheme. Finally, the proposed controller is compared with PI and existing SMC methods through simulation and experimental setup of a 5-kW PMVG system.