Abstract: An interactive computer graphics system for free-form surface design is described in this paper, and application of cubic uniform B-splines is suggested as the fundamental method of surface modeling. In order to obtain a better approximation, the basic function with a quadruple knot at each end point is utilized.In respect of curve construction, there are only 18 columns in each of various coefficient matrices for the different numbers of vertexes and the different sequences of curve segments, and the matrix expressions of curves are also given. As a result, real benefit is gained for reducing the storage capacity and increasing the computational speed. In the inverse calculation for the vertexes 26 various composite cases are summarized, which permit to maintain the original straight line segments.It is proposed to fair the given curves by fairing the curvature sequence of the discrete vertexes, and preliminary practical experience is also given.This paper offers a simple and fast engineering algorithm for modifying of the surface data in a local region, while the surface still remains in second order continuity.In the experimental system there are 20 functional buttons （embracing the functions of coordinate transform, 3-dimensional symmetry, construction of an arbitrary section etc. ）. A success has been made in surface modeling of aircraft, automobile and ship.