Clustering is one of the classification methods for data analysis and it is one of the ways of data analysis, too. There are various methods for fuzzy clustering using optimization algorithms such as genetic algorithm and particle swarm optimization algorithm that were specified. In this paper, the combination of one of the recent optimization algorithms called Forest optimization algorithm and one of the local search methods called gradient method are used to perform fuzzy clustering. The purpose of applying the gradient method is accelerating the convergence of the used optimization algorithm. To apply the proposed method, 4 types of real data sets are used. Cluster validity measures are used to obtain and verify the accuracy of the proposed method (FOFCM). By analyzing and comparing the results of the proposed method with the results of algorithms GGAFCM (fuzzy clustering based on genetic algorithm) and PSOFCM (fuzzy clustering based on particle swarm optimization algorithm), it has been shown that the accuracy of the proposed approach is significantly increased.