Mismatch between training and testing data is a major error source for both Automatic Speech Recognition (ASR) and Automatic Speaker Identification (ASI). In this paper, we first present a statistical weighting concept to exploit the unequal sensitivity of Mel-Frequency Cepstral Coefficients (MFCC) components to against the mismatch, such as ambient noise, recording equipment, transmission channels, and inter-speaker variations. We further design a new Kullback-Leibler (KL) Distance based weighting algorithm according to the proposed weighting concept to real-world problems in which the label information is often not provided. We examine our algorithm in ASR with mismatch by different speakers and also in ASI with mismatch by channel noises. Experimental results demonstrate the effectiveness and robustness of our proposed method.