3D surface matching is fundamental for shape registration, deformable 3D non-rigid tracking, recognition and classification. In this paper we describe a novel approach for generating an efficient and optimal combined matching from multiple boundary-constrained conformal parameterizations for multiply connected domains (i.e., genus zero open surface with multiple boundaries), which always come from imperfect 3D data acquisition (holes, partial occlusions, change of pose and non-rigid deformation between scans). This optimality criterion is also used to assess how consistent each boundary is, and thus decide to enforce or relax boundary constraints across the two surfaces to be matched. The linear boundary-constrained conformal parameterization is based on the holomorphic differential forms, which map a surface with n boundaries conformally to a planar rectangle with (n - 2) horizontal slits, other two boundaries as constraints. The mapping is a diffeomorphism and intrinsic to the geometry, handles an open surface with arbitrary number of boundaries, and can be implemented as a linear system. Experimental results are given for real facial surface matching, deformable cloth non-rigid tracking, which demonstrate the efficiency of our method, especially for 3D non-rigid surfaces with significantly inconsistent boundaries.