Abstract: Optimization techniques are being applied to solve the problems of surface interpolation, approximation, smooth joining and fairing, aiming at corresponding goal functions. This paper focuses on the construction of fair surface interpolating the given mesh of curved boundaries with G² adjustment at corners and G¹ smoothness between adjacent patches. Many papers on surface blending have been presented, but almost all of them are restricted to the discussion of Bezier patches. there is no good results for B-spline surface. This paper gives a solution to the B-spline surface, allowing the surface to degenerate at corner in theory and have different parametrization along the common boundary of two patches.