Speech enhancement has been proposed to reduce the impulsive noise whose frequency characteristic is wideband. On the other hand, it is challenging to reduce the ringing sound, which is narrowband in impulsive noise. Therefore, we propose the modeling of the ringing sound and its estimation by a linear predictor (LP). However, it is difficult to estimate the ringing sound only in noisy speech due to the auto-correlation property of speech. The proposed system adopts the 4th order momentbased adaptive algorithm by noticing the difference between the 4th order statistics of speech and impulsive noise. The brief analysis and simulation results show that the proposed system has the potential to reduce ringing sound while keeping the quality of enhanced speech.