Many of standard classification algorithms usually assume that the training examples are evenly distributed among different classes. However, unbalanced data sets often appear in many applications. As a simple, effective categorization method, kNN is widely used, but it suffers from biased data sets, too. In developing the Prototype of Internet Information Security for Shanghai Council of Information and Security, we detect that when training data set is biased, almost all test documents of some rare categories are classified into common ones. To alleviate such a misfortune, we propose a novel concept, critical point (CP), and adapt traditional kNN by integrating CP's approximate value, LB or UB, training number with decision rules. Exhaustive experiments illustrate that the adapted kNN achieves significant classification performance improvement on biased corpora.