In geometric design, it is often required to improve the parametrization of a curve to an optimal one. In this paper, we develop a set of functions, called representation set, that represent a given Bezier curve. Then, the optimal parametrization curve can be selected in the representation set. For a polynomial Bezier curve, its representation set is deduced by polynomial and rational reparameterization, respectively. For a rational Bezier curve, the representation set is calculated by a general degree elevation. Some important cases are presented to demonstrate the generation of the representation set geometrically. Moreover, we illustrate some examples which seek the optimal parametrization curve from its representation set.