Abstract: In order to reduce the harm of X-ray on human body,local reconstruction is becoming one of the important studies in image reconstruction.The local reconstruction algorithm based on the special filter is studied.Reconstructing the local image by using the projection data through the region of interest(ROI),generates the unknown constant bias in the reconstructed image in general.By making continuation along the radial direction,the unknown projections are derived from the projections in the ROI.And by reconstructing from the modified projection,the local reconstructed image is improved.The error analysis of this method based on the special filter is derived and this algorithm is implemented in fan beam reconstruction.According to the numerical experiment,the conclusion is obtained that this algorithm is also available to fan beam reconstruction problem.