Network traffic in cloud computing is characterized by a large volume of data, with potential high dimensionality and high levels of redundancy. “Big data” not only retard the execution process of intrusion detection systems (IDS) but they can also lead to unsatisfactory classification accuracy. The efficient correlation-based feature selection (ECOFS) approach proposed in this paper, can handle linearly and nonlinearly dependent data and it can eliminate redundant and irrelevant features. Its effectiveness has been evaluated through its employment in an intrusion detection system. A Libsvm-IDS has been built to operate using the features selected by the proposed ECOFS algorithm. The performance of the hybrid Libsvm-IDS + ECOFS approach has been evaluated using two well-known intrusion detection evaluation datasets, namely the KDD Cup 99 and the NSL-KDD. The evaluation results show that our ECOFS algorithm selects the smallest number of features, resulting in the lowest computational cost for the Libsvm-IDS, without any performance compromise. In fact, our algorithm has achieved higher accuracy compared with two well established methods.