This paper presents the Kalman filter of Synthetic Aperture Radar (SAR) images for noise reduction. Numerical methods have been proposed to suppress speckle in SAR images. SAR images have not only speckles which have the characteristic of a randam multiplicative noise but also additive noise such as receiver thermal noise. We used the Kalman filter which takes into acount both multiplicative noise and additive noise. The experiment results on the test images proved effectivity of the proposed method for both multiplivative and additive noise reduction. This method were also applied on SAR image.