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In view of the estimation problem of the priori signal-to-noise ratio (SNR) estimation in single-channel speech enhancement algorithm, a novel method based on the further information is proposed. In this paper, the information from the post frame is considered in obtaining priori SNR of the current frame. Firstly, the original priori SNR is achieved by the decision directed (DD) algorithm. secondly, in order to solve the smoothness drawback of Two-Step Noise Reduction (TSNR) method, we utilize the correlation of the inter-frame and introduce speech information from the post frame to refine the estimation priori SNR. Lastly, to track noisy speech change more quickly, a self-adaptive averaging factor is introduced by the minimum mean-squared error (MMSE) estimator. The proposed algorithm has good performance in reducing the speech distortion while the advantages in noise suppression are kept. The simulation experiment results show that the performance of proposed algorithm is superior than TSNR algorithm under various noise conditions.