The purpose of this research is to construct a surface 1) passing through all unorganized data points, 2) with G¹ -continuity and 3) with the minimum square-sum of the principal curvatures \kappa_1^2 + \kappa_2^2 over the surface. In order to construct surfaces with these three characteristics, we construct the triangular mesh spanning the data points, cover it with Bezier patches, achieve continuity between patches, and minimize the curvature to prevent the surfaces from having flat places and unnecessary undulations. The performance of the proposed method is evaluated by computational experiments.