In the medical field, successful classification of microarray gene expression data is of major importance for cancer diagnosis. However, due to the profusion of genes number, the performance of classifying DNA microarray gene expression data using statistical algorithms is often limited. Recently, there has been an important increase in the studies on the utilization of artificial intelligence methods, for the purpose of classifying large-scale data. In this context, a hybrid approach based on the adaptive neuro-fuzzy inference system (ANFIS), the fuzzy c-means clustering (FCM), and the simulated annealing (SA) algorithm is proposed in this study. The proposed method is applied to classify five different cancer datasets (i.e., lung cancer, central nervous system cancer, brain cancer, endometrial cancer, and prostate cancer). The backpropagation algorithm, hybrid algorithm, genetic algorithm, and the other statistical methods such as Bayesian network, support vector machine, and J48 decision tree are used to compare the proposed approach's performance to other algorithms. The results show that the performance of training FCM-based ANFIS using SA algorithm for classifying all the cancer datasets becomes more successful with the average accuracy rate of 96.28% and the results of the other methods are also satisfactory. The proposed method gives more effective results than the others for classifying DNA microarray cancer gene expression data.