X-ray Computed Tomograyphy (CT) has been studied and applied for several decades, and its analytical inversion method gives perfectly reconstructed image in ideal cases. However, in reconstruction of image with metal prostheses, such as dental implants, traditional analytical inversion of radon transform can cause severe streak artifact called metal artifact. For the metal artifact reduction (MAR), we propose an algorithm using linear interpolation (LI) and FOCUSS. LI reduces metal artifact by smoothing inconsistency of measured sinogram, however, with LI, reconstructed image lost most information about metallic implants. FOCUSS is an optimization method based on L1 minimization. As L1 minimization gives sparse solution, we could recover the vanished metallic object by applying FOCUSS. The experiments had performed for simulation and real dental CT data, and we could reconstruct the image without most of metal artifacts and loss of image.