The frequency coupling between a modular multilevel converter (MMC) and the power grid will affect the impedance characteristics of the converter. Conventional research does not consider the frequency coupling, causing that the impedance model is inaccurate. This is a problem for the analysis of the impedance characteristics of the system. In this paper, a full-order impedance model of MMC considering frequency coupling is established, and then the stability of the system is analyzed. An optimization scheme of MMC impedance based on a notch filter is proposed to solve the stability problem of a weak grid interconnection system. Analysis is made on the reason that the traditional impedance modeling of MMC cannot find the actual low-frequency oscillation effectively, and the generation mechanism and influence degree of frequency coupling in MMC modeling are studied. From the generation mechanism, the small signal model and variable relationship are established, and the full-order impedance model of MMC with frequency coupling is derived. Based on the full-order model, a system impedance optimization scheme based on notch is proposed. This effectively solves the problem of low frequency oscillation and stability analysis of an MMC weak network interconnection system. The simulation results verify the accuracy of the full-order impedance model of the MMC under coupling and the feasibility of the low frequency oscillation impedance optimization.