One in every eight women is susceptible to breast cancer, at some point of time in her life. Early detection and effective treatment is the only rescue to reduce breast cancer mortality. Accurate classification of a breast cancer tumor is an important task in medical diagnosis. Machine learning techniques are gaining importance in medical diagnosis because of their classification capability. In this paper, we propose a new, Genetically Optimized Neural Network (GONN) algorithm, for solving classification problems. We evolve a neural network genetically to optimize its architecture (structure and weight) for classification. We introduce new crossover and mutation operators which differ from standard crossover and mutation operators to reduce the destructive nature of these operators. We use the GONN algorithm to classify breast cancer tumors as benign or malignant. To demonstrate our results, we had taken the WBCD database from UCI Machine Learning repository and compared the classification accuracy, sensitivity, specificity, confusion matrix, ROC curves and AUC under ROC curves of GONN with classical model and classical back propagation model. Our algorithm gives classification accuracy of 98.24%, 99.63% and 100% for 50–50, 60–40, 70–30 training–testing partition respectively and 100% for 10 fold cross validation. The results show that our approach works well with the breast cancer database and can be a good alternative to the well-known machine learning methods.