The process of selecting features or reducing dimensionality can be viewed as a multi-objective minimization problem in which both the number of features and error rate must be minimized. While it is a multi-objective problem, current methods tend to treat feature selection as a single-objective optimization task. This paper presents enhanced multi-objective grey wolf optimizer with Lévy flight and mutation phase (LMuMOGWO) for tackling feature selection problems. The proposed approach integrates two effective operators into the existing Multi-objective Grey Wolf optimizer (MOGWO): a Lévy flight and a mutation operator. The Lévy flight, a type of random walk with jump size determined by the Lévy distribution, enhances the global search capability of MOGWO, with the objective of maximizing classification accuracy while minimizing the number of selected features. The mutation operator is integrated to add more informative features that can assist in enhancing classification accuracy. As feature selection is a binary problem, the continuous search space is converted into a binary space using the sigmoid function. To evaluate the classification performance of the selected feature subset, the proposed approach employs a wrapper-based Artificial Neural Network (ANN). The effectiveness of the LMuMOGWO is validated on 12 conventional UCI benchmark datasets and compared with two existing variants of MOGWO, BMOGWO-S (based sigmoid), BMOGWO-V (based tanh) as well as Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-objective Particle Swarm Optimization (BMOPSO). The results demonstrate that the proposed LMuMOGWO approach is capable of successfully evolving and improving a set of randomly generated solutions for a given optimization problem. Moreover, the proposed approach outperforms existing approaches in most cases in terms of classification error rate, feature reduction, and computational cost. © 2023 CRL Publishing. All rights reserved.