In the field of microarray gene expression research, the high dimension of the features with a comparatively small sample size of these data became necessary for the development of a robust and efficient feature selection method in order to perform classification task more precisely on gene expression data. We propose the hybrid feature selection (mRMRAGA) approach in this paper, which combines the minimum redundancy and maximum relevance (mRMR) with the adaptive genetic algorithm (AGA). The mRMR method is frequently used to identify the characteristics more accurately for gene and its phenotypes. Then their relevance is narrowed down which is described in pairing with its relevant feature selection. This approach is known as Minimum Redundancy and Maximum Relevance. The Genetic Algorithm (GA) has been propelled with the procedure of natural selection and it is based on heuristic search method. And the adaptive genetic algorithm is improvised one which gives better performance. We have conducted an experiment on four benchmarked dataset using our proposed approach and then classified using four well-known classification approaches. The accuracy was measured and observed that it gives better performance compared to the other conventional feature selection methods.