Summary: Line detection is very important in image processing. In this paper, a new randomized algorithm for detecting lines is presented. The proposed algorithm is quite different from the previous parameter--based methods which vote on the parameter space. Our proposed novel algorithm does not need extra storage to maintain an accumulator array for representing parameter space. The main concept used in the proposed algorithm is that we first randomly select three edge points in the image and use a distance criterion to determine whether there is a candidate line in the image; after finding that candidate line, we apply an evidence--collecting process to further determine whether the candidate line is the desired line. Some experiments have been carried out to demonstrate the computational and robust advantages of the proposed algorithm when compared with the previous algorithms.