The purpose of this study is to help a bank to build a cross-selling model to score the propensity of a credit card customer to take up a home loan. In order to guarantee the prediction accuracy and enhance the model comprehensibility, it is quite necessary to select out salient features and representative training samples efficiently. A new framework that coordinates feature selection and sample selection together is built. The criteria of optimal feature selection and the method of sample selection are designed. Experiments on a real bank dataset show that the new algorithm obtains higher value of the area under ROC curves, and reveals more valuable business insights.