This paper presents a novel method for current control for a modular multilevel converter (MMC). The proposed current control methodology is based on a modified sliding mode control (SMC) with proportional and integral (PI) sliding surface which allows fast transient responses and improves the robustness of the MMC control performance. As the proposed method is derived via Lyapunov direct method, the closed-loop stability is ensured and results in globally asymptotically stable. Furthermore, the reaching time is also guaranteed by the proposed method, leading to fast transient responses. The proposed method is validated by comparing with some existing methods, which are proportional integral controller and conventional SMC, via offline and hardware-in-loop (HIL) simulations where a 10 MW, medium-voltage MMC system is tested. According to these results, the proposed method is able to provide fast transient responses, zero overshoot, and robustness to the weak grid and short-circuit conditions.