Abstract: Given a set of non-intersecting B-spline curves or intersecting B-spline curves which satisfy certain constraints, the B-spline surfaces are constructed to interpolate these curves, such that they are the boundary geodesics of the constructed surfaces.The control points of interpolating surfaces are determined in two steps.Firstly, based on the theory of products and degree raising of B-spline, the control points related with interpolation conditions are computed explicitly.Secondly, other free control points of the surfaces are determined by minimizing the Dirichlet energy.The constructed surfaces have such advantages as low degrees and easily-controlled shape, and the correctness and validity of the proposed method is demonstrated by the computational examples.