The modular multilevel converter (MMC) has emerged as a promising solution for the grid integration of energy, due to its advantages. However, the complicated internal dynamics of MMC, like circulating current and submodule capacitor voltage ripples have a great influence on operation stability. To analyze the stability, this paper applies impedance-based analytical approach based on a new equivalent model that considers internal dynamics. Unlike existing analysis, this paper (i) represents the effect of internal dynamics on the output characteristics by the equivalent series impedances, and (ii) focuses on the effect of equivalent impedance on stability, rather than overall impedance. Therefore, the proposed method offers a more intuitive and accurate analysis of the effect of internal dynamics on stability with fewer repetitive modeling processes. As a result, it can effectively obtain the analytical formula of resonant frequencies with potential threats to operating stability and analyze the mechanism behind low-frequency oscillation caused by MMC internal dynamics. Finally, detailed simulations and experiments verify the effectiveness of the proposed model and analysis results.