The similarity measures between SAR images are the basis for target recognition, classification, image registration and so on. The interpretation of SAR images can be improved obviously by defining reasonable and reliably similarity measure. In this paper, a confidence interval of similarity and the method of constructing credibility are proposed based on the characteristics of image contours. Firstly, the similarity measure is obtained by fuzzifying the uncertain contours in SAR images. Then, the confidence interval of the measure as well as the definition of credibility at a given confidence level are got by analyzing the distribution function of fuzzy model. The experimental results demonstrate that the proposed similarity measure between a given pair of images is robust to the location of image contours. Besides, it can also provide reasonable similarity with credibility of the fractured and multi-edged contours, which has not been presented by other methods. Moreover, it is consistent with human visual perception.