Intrusion detection system (IDS) is used to monitor the intrusions or suspicious actions over the network traffic data or in the computer system. In this paper, we propose an IDS for identifying the intrusion over the network traffic data. As the network traffic data are continuous in nature, we used the Gaussian Naïve Bayes classification approach with the IDS to deduct the intrusions. We used the Kyoto dataset to evaluate the performance of the proposed approach. The results show that the proposed approach have better accuracy of intrusion detection, high intrusion detection rate, and low false alarm rate than the existing approaches.