The real-time simulation of modular multilevel converter (MMC) is essential to the evaluation and validation of its control and protection systems. Moreover, the dynamics at both sub-module level and system-level are expected from the real-time simulations of MMCs. To achieve this objective, this paper proposes the shifted phasor modeling (SPM) of the MMC by representing each sub-module with a Thevenin equivalent circuit that is derived using shifted phasors with improved accuracy. The efficiency of the SPM is guaranteed by modeling each arm as a switch-dependent Thevenin equivalent circuit. The computational burden remains almost unchanged even when the number of sub-modules increases considerably. The proposed model is materialized using field programmable gate array. And, thus the real-time simulation of MMC-based DC grids can be realized to capture the dynamics at the system level as well as the submodule level. The effectiveness of this paper has been validated in terms of both accuracy and efficiency on a two-terminal MMC-based low-voltage direct current system