To overcome the shortcoming that the Non-negativity And Support constraint Recursive Inverse Filtering (NAS-RIF) algorithm is noise-sensitive and time-consuming, an improved NAS-RIF algorithm for blind restoration was proposed. Firstly, a new cost function of the NAS-RIF algorithm was introduced, and then the noise resistance ability and the restoration effect were both improved. Secondly, in order to enhance computational efficiency of the algorithm, after decomposed by Haar wavelet transform, only degraded image in low frequency sub-bands was restored with the NAS-RIF algorithm, while information in high frequency sub-bands was predicted from the restored image of low frequency sub-bands by interband prediction. Finally, an interband prediction based on Minimum Mean Square Error (MMSE) was presented to guarantee the accuracy of the predicted information in high frequency sub-bands. The experiments on synthetic degraded images and real images were performed, and the Signal-to-Noise Ratio (SNR) gain by proposed algorithm were 5.2216 dB and 8.1039 dB respectively. The experimental results demonstrate that the proposed algorithm not only preserves image edges, but also has good performance in noise suppression. In addition, the computational efficiency of the proposed algorithm is greatly enhanced.