This study presents a comprehensive method for designing a multifocal contact lens (MCL) with Snell's law and non-uniform rational B-spline (NURBS) curves. Instead of using thin lens approximation, general mathematical formulas have been developed to achieve the accurate coordinates of points on the anterior lens surface profile of the MCL to meet various given optical power distributions. Then the NURBS curve is adjusted to fit these data points to obtain the smooth front lens surface profile. This method not only improves the accuracy of the optical power profiles of MCLs but also reduces the spherical aberration in near/distance optical zones. The experimental results show that the power profiles of soft MCLs agree with those of the simulation results and original design requirements. The proposed method has been proven for the MCL design, and it can be feasibly applied in complex optical lens designs.