This paper proposes a novel numerical scheme based on an improved charge simulation method for computing conformal mappings of bounded multiply connected domains. The core of the method reformulates the mapping problem into a constraint system constructed via charge simulation. This system is then solved efficiently using the symmetric successive over-relaxation incomplete Cholesky conjugate gradient method, which is particularly well-suited for handling the ill-conditioned systems inherent to such problems. Numerical experiments show that our method achieves significantly higher accuracy and improved convergence rates compared to the conventional Gauss-Seidel iteration. The results confirm the robustness and practical potential of the proposed framework, establishing it as an efficient and reliable tool for computing conformal mappings of domains with high connectivity and complex geometry.