The challenging task of medical diagnosis based on machine learning techniques requires an inherent bias, i.e., the diagnosis should favor the "ill" class over the "healthy" class, since misdiagnosing a patient as a healthy person may delay the therapy and aggravate the illness. Therefore, the objective in this task is not to improve the overall accuracy of the classification, but to focus on improving the sensitivity (the accuracy of the "ill" class) while maintaining an acceptable specificity (the accuracy of the "healthy" class). Some current methods adopt roundabout ways to impose a certain bias toward the important class, i.e., they try to utilize some intermediate factors to influence the classification. However, it remains uncertain whether these methods can improve the classification performance systematically. In this paper, by engaging a novel learning tool, the biased minimax probability machine (BMPM), we deal with the issue in a more elegant way and directly achieve the objective of appropriate medical diagnosis. More specifically, the BMPM directly controls the worst case accuracies to incorporate a bias toward the "ill" class. Moreover, in a distribution-free way, the BMPM derives the decision rule in such a way as to maximize the worst case sensitivity while maintaining an acceptable worst case specificity. By directly controlling the accuracies, the BMPM provides a more rigorous way to handle medical diagnosis; by deriving a distribution-free decision rule, the BMPM distinguishes itself from a large family of classifiers, namely, the generative classifiers, where an assumption on the data distribution is necessary. We evaluate the performance of the model and compare it with three traditional classifiers: the k-nearest neighbor, the naive Bayesian, and the C4.5. The test results on two medical datasets, the breast-cancer dataset and the heart disease dataset, show that the BMPM outperforms the other three models.