According to the Randomized Circle Detection (RCD) algorithm, the circle parameters needed to be calculated four times for each four points sampled randomly. A fast randomized algorithm for detecting circles was presented. If the distance between one point and the boundary of the circle determined by the other three points was bigger than a certain threshold in the process of judging whether the four points could determine a candidate circle, the randomized sampling and computation should be carried on again. The proposed algorithm largely decreased the calculation times of circle parameters by the new threshold. It affirmed the candidate circle for true circle to apply a quick evidence-collecting process. Some synthetic images with different levels of noises and real images were taken to test the performance. Experimental results demonstrate that the proposed algorithm can detect circles more quickly than RCD, and has a strong robustness.