The filtered back projection in the image reconstruction algorithms for the clinic computed tomography system has been widely used. Noise of the reconstructed image was examined under the input noise for parallel and fan beam geometries. The reconstruction images of $512{ imes}512$ size were carried out under 360 and 720 projection by the Visual C++ for parallel beam and fan beam, respectively, and those agreed with the original Shepp-Logan head phantom very much. Noise was generated because of intrinsic restriction (finite number of projections) for the image reconstruction algorithm, filtered back projection, when no input noise was applied. Because the result noise was rapidly increased under 0.5% input noise ratio, technologies for reducing noise in CT system and image processing is important.