Kalman algorithms have been widely applied, for instance in single-channel speech enhancement. However, when carrying out Kalman smoothing, computational cost and data storage requirements are two specific problems. A dual-filter-based smoother is proposed and used in the framework of speech enhancement. Our approach comprises a forward-in-time Kalman filter and a backward-in-time Kalman filter. Both filters are based on their respective forward-in-time linear prediction (LP) model and backward-in-time LP model. This method does not require as large a storage space as a standard Kalman smoother does. The algorithm is evaluated by considering a speech signal embedded in a white Gaussian noise. Simulation results show that the proposed algorithm provides a higher improvement of signal-to-noise ratio (SNR) than Kalman filtering.