In this paper, a mixture interacting multiple model (MIMM) algorithm is proposed to enhance speech contaminated by additive nonstationary noise. In this approach, a mixture hidden filter model (HFM) is used to model the clean speech and the noise process is modeled by a single hidden filter. The MIMM algorithm, however. needs large computation time because it is a recursive method based on multiple Kalman filters with mixture HFM. Thereby, a computationally efficient implementation of the algorithm is developed by exploiting the structure of the Kalman filtering equation. The simulation results show that the proposed method offers performance gain compared to the previous results in [4,5] with slightly increased complexity.