Abstract: Although the Conformal Finite-Difference Time Domain(C-FDTD) method significantly improves modeling accuracy for curved surfaces, its stability is constrained by grid distortion, which limits computational efficiency. To overcome this limitation, several conformal unconditionally stable algorithms have been studied. However, the conformal parameters complicate the rigorous stability proof, leaving most existing studies without solid theoretical support. In this work, we propose an efficient and stable two-dimensional Conformal Leapfrog Complying Divergence Implicit FDTD(C-LCDI-FDTD) method for solving electromagnetic scattering problems. The update equations for the transverse electric(TE) case are derived. Stability analysis, combining the von Neumann method with the Jury criterion, theoretically demonstrates the unconditional stability of the proposed algorithm. Compared with the conventional C-FDTD method, the proposed method removes the strict stability constraint, allowing larger time steps and improving computational efficiency. Moreover, in contrast to the standard LCDI-FDTD method, it avoids staircase approximation errors and provides higher modeling accuracy. Numerical examples verify the theoretical analysis, completing the cycle from proof to validation.