Abstract: In order to get the approximately arc-length parameterized rational Bézier curves, a method for reparameterization of rational Bézier curves is proposed based on a piecewise M？bius parameter transformation. This method constructs the piecewise M？bius transformation applying to the rational Bézier curve, on which the break points are chosen as the locally maximal value points of its curvature. And a metric function is defined by the deviation of new parametric speed from unit-speed with respect to L2 norm under the condition of C1 continuous parametric speed. Then the expression of this M？bius transformation is obtained by minimizing the metric function. Numerical examples show that rational Bézier curves with piecewise M？bius transformation have good parameters very close to the arc-length parameter.