A fast FBP algorithm for special density detection is given in this article. At first, reconstruction of image with incomplete data is made. Second, image is clustered and partitioned based on the density known. Lastly, the interesting area can be reconstructed exactly. The results of experiment were compared with FBP algorithm and the algorithm using geometric parameter table at the end of article. The results indicate that the algorithm is not only faster than FBP but also has no effect on the interest area reconstruction.