Integrating Power Electronics Converters (PECs)-based renewable energy sources can establish a weak grid due to the substantial inertia reduction leading to severe frequency fluctuations. In this paper, a control strategy based on the Virtual Synchronous Generator (VSG) concept is designed for a three-phase Modular Multilevel Converter (MMC) connected to a weak grid. The proposed VSG control approach improves the frequency response during transient mode, resulting in a 66.7% enhancement at the Point of Common Coupling (PCC). The proposed strategy is shaped within four control loops wherein the VSG-dependent output current control possesses the duty of enriching the MMC output current tracking capability. Focusing on the MMC output current-based transfer function, the effectiveness of this capability is guaranteed using the frequency domain analysis including the Nyquist and Bode diagrams. Moreover, a comprehensive discussion was carried out regarding the impact of VSG on the voltage of submodule capacitors and the circulating current. Simulation results in MATLAB/Simulink environment validate the accuracy and weak grid-connected MMC performance under the proposed VSG-based control technique. To further verify the superiority of the proposed strategy, two control techniques including Droop and SEBIR are compared with the VSG proposed controller.