Grid-forming converter, which mimics the frequency and voltage support behaviors of the synchronous generators, has been identified as a promising technique toward modern power system. The high penetration of grid-forming converters into power system rises large-signal stability issues during transients, which may further harm the safe and reliable operation of the modern power system. In this paper, the large-signal stability of systems with paralleled grid-forming converters is studied with the consideration of large damping effects. The detailed transient model of the paralleled system with grid-forming converters is firstly established and the concept of the uniform damping energy and the nonuniform damping energy are introduced to clarify the damping effects. On this basis, a transient stability enhancement strategy is proposed by approximately tuning the damping coefficients. Finally, simulation cases are executed to prove the validity of the proposed stability enhancement method.