DNA microarray technology is the fabrication of a single chip to contain a thousand genetic codes. Each microarray experiment can analyze many thousands of genes in parallel. The outcomes of the DNA microarray is a table/matrix, called gene expression data. Pattern recognition algorithms are widely applied to gene expression data to differentiate between health and cancerous patient samples. However, gene expression data is characterized as a high dimensional data that typically encompassed of redundant, noisy, and irrelevant genes. Datasets with such characteristics pose a challenge to machine learning algorithms. This is because they impede the training and testing process and entail high resource computations that deteriorate the classification performance. In order to avoid these pitfalls, gene selection is needed. This paper proposes a new hybrid filter-wrapper approach using robust Minimum Redundancy Maximum Relevancy (rMRMR) as a filter approach to choose the topranked genes. Modified Gray Wolf Optimizer (MGWO) is used as a wrapper approach to seek further small sets of genes. In MGWO, new optimization operators inspired by the TRIZ-inventive solution are coupled with the original GWO to increase the diversity of the population. To evaluate the performance of the proposed method, nine well-known microarray datasets are tested. The support vector machine (SVM) is employed for the classification task to estimate the goodness of the selected subset of genes. The effectiveness of TRIZ optimization operators in MGWO is evaluated by investigating the convergence behavior of GWO with and without TRIZ optimization operators. Moreover, the results of MGWO are compared with seven state-of-art gene selection methods using the same datasets based on classification accuracy and the number of selected genes. The results show that the proposed method achieves the best results in four out of nine datasets and it obtains remarkable results on the remaining datasets. The experimental results demonstrated the effectiveness of the proposed method in searching the gene search space and it was able to find the best gene combinations.