Abstract: The grid-forming grid-connected inverter（GFM-GCI） can provide the voltage and frequency support for power grids, which is beneficial to grid stability improvement. Firstly, aiming at the transient synchronization stability problem of GFM-GCI, the influence mechanism of GFM-GCI control parameters on the transient synchronization stability is qualitatively analyzed from the perspective of energy by the equal area criterion considering the damping characteristics. Secondly, the explicit analytical solution of the nonlinear second-order differential equation of the power angle is obtained by using the multi-scale method in perturbation theory, and the influence of control parameters on the GFM-GCI transient synchronization stability is quantitatively analyzed. Then, based on the analytical solution and transient synchronization stability boundary, a control parameter design method for GFM-GCI transient synchronization stability is presented. The proposed control parameter design method is less conservative than the existing traditional transient analysis methods. Finally, the validity of the theoretical analysis, the analytical model and the proposed control parameters design method is verified by simulation and experiment.