Abstract: In order to solve the problems of traditional Coons surfaces not being able to handle guide curves, and Gordon surfaces requiring the interpolation of bi-directional isoparametric curves which brings in a large number of control points, an extended Coons surface algorithm with guide curves was proposed for the needs of practical engineering design. Firstly, a Coons surface is generated based on the given boundary curves, and the offset vectors are obtained by uniformly sampling the guide curves and projecting the sampling points onto the surface. Then, the offset vectors are fitted by the least squares method, and the smooth energy constraints of the control points are added to generate the offset surface compatible with the base surface. Finally, the offset surface is superimposed onto the base Coons surface to obtain the extended Coons surface with guide curves. The results show that the proposed algorithm is able to approximate the guide curves within a tolerance of 5 mm compared with the traditional Coons surface, and the control points are reduced by about 40% compared with those of the traditional Gordon surface, which verifies the effectiveness of the algorithm.