Virtual synchronous generator (VSG) is deemed to be the key foundation for the future low inertia power system for its superiority to provide flexible inertia support. However, complicated dynamic frequency interaction, active power oscillation, and inappropriate transient active power-sharing will occur when VSGs are widely applied. Center of Inertia (COI) is introduced for solving these problems. But the calculation of COI frequency relies on global communication and a centralized controller, which results in high communication costs and complexity, and reduces the system reliability. This paper proposes a distributed control method via COI frequency for multi-VSG grids. The COI frequency estimator is designed based on dynamic consensus control. Communication between adjacent neighbors is required, which improves reliability and reduces communication costs. The stability of the proposed control method is proved and the feasible range of the control parameter is presented in this paper. Simulations and experiments are carried out to verify the effectiveness and feasibility.