The purpose of this paper is to develop a method of eliminating CT image artifacts generated by objects extending outside the scan field of view, such as obese or inadequately positioned patients. CT projection data are measured only within the scan field of view and thus are abruptly discontinuous at the projection boundaries if the scanned object extends outside the scan field of view. This data discontinuity causes an artifact that consists of a bright peripheral band that obscures objects near the boundary of the scan field of view. An adaptive mathematical extrapolation scheme with low computational expense was applied to reduce the data discontinuity prior to convolution in a filtered backprojection reconstruction. Despite extended projection length, the convolution length was not increased and thus the reconstruction time was not affected. Raw projection data from ten patients whose bodies extended beyond the scan field of view were reconstructed using a conventional method and our extended reconstruction method. Limitations of the algorithm are investigated and extensions for further improvement are discussed. The images reconstructed by conventional filtered backprojection demonstrated peripheral bright-band artifacts near the boundary of the scan field of view. Images reconstructed with our technique were free of such artifacts and clearly showed the anatomy at the periphery of the scan field of view with correct attenuation values. We conclude that bright-band artifacts generated by obese patients whose bodies extend beyond the scan field of view were eliminated with our reconstruction method, which reduces boundary data discontinuity. The algorithm can be generalized to objects with inhomogeneous peripheral density and to true "Region of Interest Reconstruction" from truncated projections.