In this paper, a robust feature compensation method is proposed for improving the performance of speech recognition. The proposed method is incorporated into the auto-regressive moving average (ARMA) based feature compensation. We employ variable weights for the ARMA filter according to the degree of speech activity, and pass the normalized cepstral sequence through the weighted ARMA filter. Additionally when normalizing the cepstral sequences in training, the cepstral means and variances are estimated from total training utterances. Experimental results show the proposed method significantly improves the speech recognition performance in the noisy and reverberant environments.