To compensate for image artifacts introduced in approximate cone-beam reconstruction, exact cone-beam reconstruction algorithms are being developed for medical x-ray CT. Although the exact cone-beam approach is theoretically error-free, it is subject to image artifacts due to the discrete nature of numerical implementation. We report a study on image artifacts associated with the Grangeat algorithm as applied to a circular scanning locus. Three types of artifacts are found, which are thorn, wrinkle, and V-shaped artifacts. The thorn pattern is created by inappropriate extrapolation into the shadow zone in the radon domain. If the shadow zone is filled in with continuous data, the thorn artifacts along the boundary of the shadow zone can be removed. The wrinkle appearance arises if interpolated first derivatives of the radon data are not smooth between adjacent detector planes. In particular, the nearest-neighbor interpolation method should not be used. If the number of projections is not small, the bilinear interpolation method is effective to suppress the wrinkle artifacts. The V-shaped artifacts on the meridian plane come from the line integrations through the transition zones where derivative data change abruptly. Two remedies are to increase the sampling rate and suppress data noise.