Recently, with the development of hardware and software technology related with image information delivery, the demand for various multimedia service has increased. But, the process of treating, sending, and storing image signals generates image degradation by various external causes. The main cause of image degradation is noise. image is mostly damaged by AWGN (additive white Gaussian noise). Therefore, there have been active researches on noise elimination. This paper, to reduce the effects of AWGN added to the image, suggests a noise-eliminating algorithm which is excellent in low-frequency and high-frequency characteristics in space. And, this paper, through simulation techniques, compared the result of the suggested algorithm with those of the existing methods. And, to evaluate the performance of it, PSNR (peak signal to noise ratio) was used.