An intrusion detection system (IDS) is either a part of a software or hardware environment that monitors data and analyses it to identify any attacks made against a system or a network. Traditional IDS approaches make the system more complicated and less efficient, because the analytical properties process is difficult and time-consuming. This is because the procedure is complex. Therefore, this research work focuses on a network intrusion detection and classification (NIDCS) system using a modified convolutional neural network (MCNN) with recursive feature elimination (RFE). Initially, the dataset is balanced with the help of the local outlier factor (LOF), which finds anomalies and outliers by comparing the amount of deviation that a single data point has with the amount of deviation that its neighbors have. Then, a feature extraction selection approach named RFE is applied to eliminate the weakest features until the desired number of features is achieved. Finally, the optimal features are trained with the MCNN classifier, which classifies intrusions like probe, denial-of-service (DoS), remote-to-user (R2U), user-to-root (U2R), and identifies normal data. The proposed NIDCS system resulted in higher performance with 99.3% accuracy and a 3.02 false alarm rate (FAR) as equated to state-of-the-art NIDCS approaches such as deep neural networks (DNN), ResNet, and gravitational search algorithms (GSA).