In this paper， we mainly apply the breast cancer data from University of Wisconsin System to predict breast cancer using penalized logistic regression. Firstly， the ten indicators related to breast cancer are selected as the predictor variables. Then， logistic regression， the LASSO penalized logistic regression， the L2 penalized logistic regression and the elastic net penalized logistic regression are used as the four classifiers. 75% of the data set is used as the training set to build models. Finally， 25% test set， a confusion matrix and a ROC curve are used to evaluate their prediction accuracy. The results show that the LASSO penalized logistic regression performs best， whose prediction accuracy reaches 97.18%. The prediction performance of the elastic net penalized logistic regression changes with the increase of α， especially when α=0.9， the corresponding prediction accuracy is 97.18%， as good as that of LASSO penalized logistic regression. The L2 penalized logistic regression ranks the third and logistic regression performs the worst in prediction performance. Therefore， for the diagnosis of breast tumors， doctors can apply the LASSO penalized logistic regression and the elastic net penalized logistic regression to improve the diagnostic accuracy.