Classification is always the key point in the field of remote sensing. Fuzzy c-Means is a traditional clustering algorithm that has been widely used in fuzzy clustering. However, this algorithm usually has some weaknesses, such as the problems of falling into a local minimum, and it needs much time to accomplish the classification for a large number of data. In order to overcome these shortcomings and increase the classification accuracy, Gustafson-Kessel (GK) and Gath-Geva (GG) algorithms are proposed to improve the traditional FCM algorithm which adopts Euclidean distance norm in this paper. The experimental result shows that these two methods are able to detect clusters of varying shapes, sizes and densities which FCM cannot do. Moreover, they can improve the classification accuracy of remote sensing images.