The process of dimensionality reduction is a crucial solution to deal with the dimensionality problem that may be faced when dealing with the majority of machine learning techniques. This paper proposes an enhanced hybrid metaheuristic approach using grey wolf optimizer (GWO) and whale optimization algorithm (WOA) to develop a wrapper-based feature selection method. The main objective of the proposed technique is to alleviate the drawbacks of both algorithms, including immature convergence and stagnation to local optima (LO). The hybridization is done with improvements in the mechanisms of both algorithms. To confirm the stability of the proposed approach, 18 well-known datasets are employed from the UCI repository. Furthermore, the classification accuracy, number of selected features, fitness values, and run time matrices are collected and compared with a set of well-known feature selection approaches in the literature. The results show the superiority of the proposed approach compared with both GWO and WOA. The results also show that the proposed hybrid technique outperforms other state-of-the-art approaches, significantly.