Proposed GA-BFSS and logistic regression based intrusion detection system Enormous growth in Internet Technology accelerates sharing of limitless data, service and resources. But along with the innumerable benefits of Internet, a number of serious issues have also taken birth regarding data security, system security and user privacy. A numbers of intruders attempt to gain unauthorized access into computer network. Intrusion Detection System (IDS) is a stronger strategy to provide security. In this paper, we have proposed an efficient IDS by selecting relevant futures from NSL-KDD dataset and using Logistic Regression (LR) based classifier. To decrease memory space and learning time, a feature selection method is required. In this paper we have selected a number of feature sets, using the approach of Genetic Algorithm (GA), with our proposed fitness score based on Mutual Correlation. From the number of feature sets, we have selected the fittest set of features using our proposed Best Feature Set Selection (BFSS) method. After selecting the most relevant features from NSL-KDD data set, we used LR based classification. Thus, an efficient IDS is created by applying the concept of GA with BFSS for feature selection and LR for classification to detect network intrusions.