Abstract: Existing pixe-l level algorithms for rasterizing parametric curves aimed at finding in single step an optimum step-length for the whole curve．We propose a new approach，its result is verified to be better than those of the existing ones and is proved to be optimum．Thus the problem of oversampling has got an improved solution so far for the traditional single-step algorithm．To make further progress，a double-step algorithm that uses only integer arithmetic is presented．The number of points computed by this algorithm is reduced by half by doubling the step-length in case that the same pixels are set as the single-step algorithms do．The results of performance tests show that the ratio of the number of effective points to the number of all points computed is nearly 100％，which means that the problem of oversampling is solved even better．The results also show that the time needed by the new algorithm for rasterizing curves is much less than that needed by the other algorithms．The new algorithm can be used to draw any parametric curves．