According to the Cisco Visual Networking Index, the annual global network traffic is growing consistently and would reach 3.3 ZB by 2021. The percentage of attack traffic is also increasing with the same rate in network traffic. The rapidly growing unauthorized activities on a network need a time efficient intrusion detection system with the high detection rate of attacks. Here, we propose a modification in the recall phase of a well-known method, enhanced fuzzy min–max neural network (EFMN), with the aim to achieve high detection rate of attacks in the minimum training and recall time. The modified-EFMN is employed for the detection of network attacks and the results are compared with the standard SVM, rule-based, and neuro-fuzzy-based classifiers on the benchmark datasets. We demonstrate that the proposed method provides a time efficient intrusion detection with the competitive detection rate. We also discuss the parallel implementation of the modified-EFMN on the modern Graphics Processing Units (GPUs) to accelerate its performance further for the heavily growing network traffic. The NVIDIA GeForce GTX 750 Ti with 640 cores is used for the implementation.