This article analyzes the parametric effect of the dc-link voltage controller (DVC) on the transient stability of grid-forming (GFM) inverters. It is found that the decrease of the proportional gain of DVC may lead to the loss of synchronism (LOS) even if the system is locally stable at the new equilibrium point (EP) after disturbance. Its physical insight is attributed to the unstable limit cycle (ULC) in the phase space according to the bifurcation theory. The GFM inverters whose operating point locates outside of ULC will lose synchronism with the grid. The decrease of the proportional gain of DVC will diminish the ULC, resulting in fewer operating points converging to the new EP and a higher risk of LOS. This bifurcation-based analysis provides a novel perspective for investigating the mechanism of parametric effect for the high-order nonlinear system, which is the article's main contribution. The parametric effect of the integral gain of DVC is also analyzed. A holistic parametric space partition for designing DVC is then drawn from the analysis, and a parametric configuration guideline is provided. The theoretical findings are validated by experimental tests.