Cancer is a deadly disease that occurs due to rapid and uncontrolled cell growth. In this article, a machine learning (ML) algorithm is proposed to diagnose different cancer diseases from big data. The algorithm comprises a two-stage hybrid feature selection. In the first stage, an overall ranker is initiated to combine the results of three filter-based feature evaluation methods, namely, chi-squared, -statistic, and mutual information (MI). The features are then ordered according to this combination. In the second stage, the modified wrapper-based sequential forward selection is utilized to discover the optimal feature subset, using ML models such as support vector machine (SVM), decision tree (DT), random forest (RF), and -nearest neighbor (NN) classifiers. To examine the proposed algorithm, many tests have been carried out on four cancerous microarray datasets, employing in the process 10-fold cross-validation and hyperparameter tuning. The performance of the algorithm is evaluated by calculating the diagnostic accuracy. The results indicate that for the leukemia dataset, both SVM and KNN models register the highest accuracy at 100% using only 5 features. For the ovarian cancer dataset, the SVM model achieves the highest accuracy at 100% using only 6 features. For the small round blue cell tumor (SRBCT) dataset, the SVM model also achieves the highest accuracy at 100% using only 8 features. For the lung cancer dataset, the SVM model also achieves the highest accuracy at 99.57% using 19 features. By comparing with other algorithms, the results obtained from the proposed algorithm are superior in terms of the number of selected features and diagnostic accuracy.