There have been a considerable amount of work conducted to design multi-coil arrays (MCA) for human brain shimming at 3T. Menese, et al. has proposed a numerical method to find optimal geometry and positions of shimming coils, although they are difficult to be implemented . In this work, we proposed an optimization algorithm to identify the redundancy in a surface shimming coil system. The algorithm utilized mathematical models, such as singular value decomposition (SVD) and principle component analysis (PCA) to derive the importance of each surface shimming coils in a realistic shimming environment. We tested the algorithm using a set of evenly distributed surface shimming coils with a cylindrical coverage. Brain field maps from the Human Connectome Project (HCP) were used to test the efficacy of the algorithm. We successfully demonstrated that 95% of the shimming capability can be preserved with 30% reduction in shimming channels using the proposed algorithm.