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This paper describes a method to significantly reduce the complexity of continuous density HMM with only a small degradation in performance. The proposed method is noise-robust and may perform even better than the standard algorithm if training and testing noise conditions are not matched. The method is based on approximating the variance vectors of the Gaussian kernels by a vector quantization (VQ) codebook of a small size. The quantization of the variance vectors is done using an information theoretic distortion measure. Closed form expressions are given for the computation of the VQ codebook and the superiority of the proposed distortion measure over the Euclidean distance is demonstrated. The effectiveness of the proposed method is shown using the connected TI digits database and a noisy version of it. For the connected TI digit database, the proposed method shows that by quantizing the variance to 16 levels we can maintain recognition performance within 1% degradation of the original VR system. In comparison, with Euclidean distortion, a size 256 codebook is needed for a similar error rate.