Abstract: To solve the reverse active design problem in computer aided design, an algorithm for constructing discrete surface with arbitrary multiple spatial discrete curves as geodesics is proposed. Firstly, the geometrical variables of the curve are discretized by using the idea of osculating circle, and then the formula of discrete surface which satisfies the constraint conditions is derived by means of local interpolation and the characteristics of geodesics. Finally, the formula for constructing the discrete surface with B-spline as the measurement function is given. The reverse active design test results show that this algorithm is feasible and has strong interactivity, the shape of surface can be adjusted by modifying the knot vector of the B-spline measurement function or the control points, therefore this algorithm has bright application prospect in garment, shoes and hats, false tooth design industry.