In order to save the time and cost of industrial development and production of anti-breast cancer drugs, a quantitative prediction model of ER$\alpha$ biological activity based on Support Vector Regression (SVR) is established. SVR is used for learning the strong nonlinear relationship between molecular descriptors and ER$\alpha$ biological activity. One-fifth of the samples are used as the test set, and the remaining samples are used as the training set to train and predict the SVR. In order to verify the accuracy of the selected model, three commonly used prediction models, BPNN, RBFNN, and ELM, are also used for network training. Their predictions are evaluated and compared by citing Mean Squared Errors and fitting coefficients. The results show that the prediction accuracy of the SVR is high, and the selection of the model is appropriate. At last, the trained SVR is used to predict the ER$\alpha$ biological activity of the unknown 50 compounds.