Fractal geometry is becoming increasingly important in the study of image characteristics. For recognition of regions and object in natural scenes, there is always a need for features, which are invariant and they provide a good set of descriptive values for the region. There are numerous methods available to estimate parameters from the image of the fractal surface. In this paper, fractal features of digital mammogram images are studied with aim of classifying breast cancer. Fractal dimensions(FD) and fractal signature(FS) are considered as different features to characterize the degree of self-similarity among the points in the clusters. The result has shown the potential usefulness of the fractal signature and fractal dimension for image analysis. The K-Means algorithm is used for classification of images. It has been found that 96% classification rate could be achieved. Keywords: Fractal dimension, Fractal signature, Mammogram, invariant- methods: data analysis.