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The application of Missing Data Technique (MDT) has shown to improve the performance of speech recognition. To apply MDT to cepstral domain, this paper presents a weighted approach to compute the reliability of cepstral feature based on sigmoid function and introduces a weighted distance algorithm. It is deduced that the reliability compensates the Gaussian variance in hidden Markov model (HMM) frame by frame to reduce the mismatch between clean-trained model and corrupted speech. Experimental evaluation using the Aurora2 database demonstrates a distinct digit error rate reduction. The main advantages of the approach are simple system implementation, low computation cost and easy to plug into other robust recognition algorithm.