This paper proposes an algorithm that adaptively estimates time-varying noise variance used in Kalman filtering for real-time speech signal enhancement. In the speech signal contaminated by white noise, the spectral components except dominant ones in high frequency band are expected to reflect the noise energy. Our approach is first to find the dominant energy bands over speech spectrum using LPC. We then calculate the average value of the actual spectral components over the high frequency region excluding the dominant energy bands and use it as the noise variance. The resulting noise variance estimate is then applied to Kalman filtering to suppress the background noise. Experimental results indicate that the proposed approach achieves a significant improvement in terms of speech enhancement over those of the conventional Kalman filtering that uses the average noise power over silence interval only. As a refinement of our results, we employ multiple-Kalman filtering with multiple noise models and improve the intelligibility.