Network intrusion is a well-studied area of cyber security. Current machine learning-based network intrusion detection systems (NIDSs) monitor network data and the patterns within those data but at the cost of presenting significant issues in terms of privacy violations which may threaten end-user privacy. Therefore, to mitigate risk and preserve a balance between security and privacy, it is imperative to protect user privacy with respect to intrusion data. Moreover, cost is a driver of a machine learning-based NIDS because such systems are increasingly being deployed on resource-limited edge devices. To solve these issues, in this paper we propose a NIDS called PCC-LSM-NIDS that is composed of a Pearson Correlation Coefficient (PCC) based feature selection algorithm and a Least Square Method (LSM) based privacy-preserving algorithm to achieve low-cost intrusion detection while providing privacy preservation for sensitive data. The proposed PCC-LSM-NIDS is tested on the benchmark intrusion database UNSW-NB15, using five popular classifiers. The experimental results show that the proposed PCC-LSM-NIDS offers advantages in terms of less computational time, while offering an appropriate degree of privacy protection.