Keyword search (KWS) systems based on automatic speech recognition lattices require sufficient amount of transcribed data. However, out of vocabulary queries are frequently encountered in low resource languages and they lower the KWS performance. One method to overcome this problem is to use confusion model (CM) that allows searching for expanded queries along with the original query. In this study, our aim is to maximize the performance criterion of the KWS system, namely the Term Weighted Value, by discriminative training of the CM. As a result of the experiments, there is 2 percent increase in the performance when the trained CM which is initialized with a random CM is used in the KWS system.