Big data is progressively being used in various areas, such as industry, financial dealing, medicine, and so on, as it can handle the challenges in processing large amounts of data. One of the data mining techniques used widely and effectively to classify big data is the MapReduce model. In this paper, an approach for the classification of big data is developed using Cuckoo–Grey wolf based Correlative Naive Bayes classifier and MapReduce Model (CGCNB-MRM). Accordingly, a novel classifier, named Cuckoo–Grey wolf based Correlative Naive Bayes classifier (CG-CNB), is designed by modifying CNB classifier with a newly developed optimization algorithm, Cuckoo–Grey Wolf based Optimization (CGWO). CGWO algorithm is designed by the effective integration of Cuckoo Search (CS) Algorithm into Grey Wolf Optimizer (GWO), to optimize the CNB model by the optimal selection of the model parameters. Finally, the proposed CGCNB-MRM approach performs the classification for each data samples based on the probability index table and the posterior probability of the data. Three metrics, such as accuracy, sensitivity, and specificity, are utilized for the performance evaluation of the proposed CGCNB-MRM approach, where it could achieve 80.7% accuracy with 84.5% sensitivity and 76.9% specificity and thus, prove its effectiveness in big data classification.