Curve-net interpolation surface is one of the most popular method in engineering design. Therefore it is supported with many commercial CAD/CAM system. However, construction algorithm of curve-net interpolation surfaces is rarely opened to the public because of its copy-right. In this paper we establish a construction algorithm of curve-net interpolation surface so called sweeping surface which especially concentrates on trajectory of cross-section curve. We also show the method which can construct sweeping surfaces as NURB or Bezier mathematical models. Surfaces having the form of standard mathematical models are very useful for the application of joining, trimming, blending etc. The proposed surface interpolation scheme consists of four steps; (1) preparation of guide curves and section curves, (2) remeshing guide curves and section curves, (3) blending section curves after deformation, and (4) determination of control points for sweeping surface using gordon method. The proposed method guarantee $G^1$-continuety, and construct the surface salifying given section curves and trajectory of section curves.