Modular multilevel converter (MMC) is widely used in high voltage direct current (HVDC). However, the multivariate and strongly nonlinear characteristics of MMC make the stable control problem become the key to their application. From the perspective of energy dissipation and circulating current suppression, the bilinear Lagrange equation in a-b-c synchronous reference frame is developed directly on the basis of the dynamic mathematical model of MMC to analyze strictly passive features of the system. Energy function for balancing capacitor voltage is designed. Combining the simple architecture of PI control, a novel passivity-based PI control method is proposed to ensure the whole system along Lagrange integration minimization trajectory. The desired trajectory fast tracking can be realized under the premise of global asymptotic stability. For the increase of converter losses generated by the circulation of MMC-HVDC, this paper designs circulating current controller of MMC to obtain arm voltage compensation in passivity-based PI control and achieves that the capacitor voltage comes to smooth and circulation is effectively suppressed. The simulation results show that the proposed method has the advantages of quick response, high stability and strong robustness. This work is supported by National Natural Science Foundation of China (No. 51207086).