Today, cancer counted as the riskier disease than the other diseases in the globe. There are many cancer forms like leukemia, skin cancer, and stomach cancer but lung and breast cancer are the most common forms that many people suffered from. Cancer is the disease that cell has grown rapidly and abnormally that is why treating it is somehow tough in some cases but it can be controlled if it is detected in the initial stage. Data-mining classification algorithms had a vital role in predicting and recognizing both benign and malignant cell. Several classifiers are available to classify the usual and unusual cells such as decision-tree, artificial-neural net, SVM, and KNN. This paper presents a systematic review about the most well-known data-mining classification algorithms for lung and breast cancer diagnose. A brief review about KDD and the data-mining concept has demonstrated. The Decision-Tree (D-Tree), ANN, Support-vector-machine, and naïve Bayes classifier that is widely utilized in the biomedical field has been reviewed along with the some algorithms such as C4.5, Cart, and Iterative -Dichotomiser 3 ‘ID3’. A comparison has been done among various reviewed papers in terms of accuracy that used various data-mining classification algorithms to propose the lung and breast cancer diagnosis system. The experimental results of the reviewed papers showed that the Multilayer Perceptron (MLP) and Logistic Regression (LR) gave a higher accuracy of 99.04% and 98.1%, respectively.