Abstract: By analyzing the relationship between different discriminative training objective function and MMI (Maximum Mutual Information) being as the separation measure, the different discriminative training objective function is unified into a discriminative training criteria based on generalized margin. The weighting function in the criteria is further discussed and two kinds of discriminative objective function are got. When the candidate path is weighted through a combination of boosted factor and the number of the misrecognition words in the candidate path, a discriminative objective function SBMMI (Soft Boosted MMI) is presented. While a single candidate word is dynamic weighted using the exponential form in which the misrecognition rate of each training statement is defined by the posterior probability of a single candidate, another discriminative objective function VWMMI (Variable Weighting MMI) is proposed. The experimental results show that compared with the soft margin estimation and boosted maximum mutual information method, the recognition accuracy of SBMMI method increases by 0.89% and 0.56% separately and VWMMI method has a 0.68% improvement upon SBMMI method.