Abstract: In order to use the rational freedom to solve the optimal parameterization of parametric curves, this paper present a fast and accurate algorithm for determining optimal parametric equation of rational parametric curve. The sufficient condition of optimal parametric equation of rational parametric curve is given firstly, that is, both ends have the same rate and the values of them are optimal; then the algorithm for finding optimal parametric equations of general rational parametric curve is proposed. Compared with other algorithms, the algorithm is simple, reliable, less amount of computation, effective, and applicable to a wide range.