Data clustering is an important part of cluster analysis. Numerous clustering algorithms based on various theories have been developed, and new algorithms continue to appear in the literature. In this paper, supposing that each cluster center is a gravity center and each data point has a constant mass, Newton's law of gravity is transformed from m/d(2) to l/d(2). According to adapted the law, we have proposed novel method called Gravitational Fuzzy clustering. The three main contributions of new algorithm can be summarized as: 1) it becomes more sophisticated technique by taking advantages of K-means, fuzzy C-means and subtractive clustering methods, 2) it removes the dependence on initial condition by taking account of the gravitation effect. 3) it improves the cluster centers by means of the gravity center of clusters. We illustrate the advantage of the resulting of gravitational approach with several examples.