Noise robustness is one of the primary challenges facing most automatic speech recognition (ASR) systems. A vast amount of research efforts on preventing the degradation of ASR performance under various noisy environments have been made during the past several years. In this paper, we consider the use of histogram equalization (HEQ) for robust ASR. In contrast to conventional methods, a novel data fitting method based on polynomial regression was presented to efficiently approximate the inverse of the cumulative density functions of speech feature vectors for HEQ. Moreover, a more elaborate attempt of using such polynomial regression models to directly characterizing the relationship between the speech feature vectors and their corresponding probability distributions, under various noise conditions, was proposed as well. All experiments were carried out on the Aurora-2 database and task. The performance of the presented methods were extensively tested and verified by comparison with the other methods. Experimental results shown that for cleancondition training, our method achieved a considerable word error rate reduction over the baseline system, and also significantly outperformed the other methods.