There are many methods to extract moving objects in a scene using background subtraction. However, most methods assume that there are no moving objects except intruders in the observing space. In this paper, we propose the iterative optimal projection method to estimate a varied background in real time from a dynamic scene with intruders. At first, background images are collected for a while, because we assume that the motion of background is well known. Then, the background images are compressed using eigenspace method to form a database. While monitoring the scene, new image is taken by a camera, and the image is projected onto the eigenspace to estimate the background. But however, the estimated image is much affected by the intruders, so the intruder region is calculated by using background subtraction with former estimated background to exclude the region from the projection. Thus the image whose intruder region is replaced by the former background is projected to eigenspace and we have updated background. We proved that the cycle converges to a correct background image and we confirmed we can calculate the right region of the object through some experiments.