With the rapid increase in intrusion attempts exhibiting nonlinear behavior, network traffic behaves unpredictably, and there is a massive feature in the problem domain, intrusion detection systems pose a complex challenge. Dealing with high-dimensional and imbalanced datasets becomes an obstacle in real-world applications like intrusion detection systems (IDS). To overcome this problem we adopted feature selection considering the classification performance and computational efficiency. In this research work, we propose MI-RFE, a hybrid feature selection method tasked with a binary class intrusion detection system that exploits the qualities of both a filter method chosen because of its speed and a wrapper method because of its relevance in search. In the first phase of our approach, we utilize Mutual Information (MI) for its computational efficiency and ability to handle nonlinear datasets to rank the features based on their importance. In the second phase, we employ recursive feature elimination (RFE) which is a machine learning-based wrapper method to further reduce the feature dimensions. Additionally, we apply the Synthetic Minority Over-sampling Technique (SMOTE) to address class imbalances in the dataset. The optimal features obtained from the proposed method were evaluated using a Decision Tree (DT), K-nearest neighbors (KNN), Random Forest (RF), and XGBOOST and these algorithms were then combined using Stacking (DT + KNN + RF + XGBoost) techniques to improve their performance. Our experimental results obtained based on the CICIDS 2017 dataset confirmed that the proposed method improves the performance and computational time. The results show that the feature is reduced from 78 to 25 while the accuracy of DT is improved from 93.94% to 99.34% and we achieve 99.92% by Stacking (DT + KNN + RF + XGBoost) using the reduced features. Keywords: MI, RFE, Stacking, SMOTE