If there are metals located in the X-ray scanned object, a point outside the metals has its range of projection angle at which projections passing through the point are disturbed by the metals. Roughly speaking, this implies that attenuation information at the point is missing in the blocked projection range. So conventional projection completion MAR algorithms to use the undisturbed projection data on the boundary of the metaltrace is less efficient in reconstructing the attenuation coefficient in detailed parts, in particular, near the metal region. In order to overcome this problem, we propose the algebraic correction technique (ACT) to utilize a pre-reconstructed interim image of the attenuation coefficient outside the metal region which is obtained by solving a linear system designed to reduce computational costs. The reconstructed interim image of the attenuation coefficient is used as prior information for MAR. Numerical simulations support that the proposed correction technique shows better performance than conventional inpainting techniques such as the total variation and the harmonic inpainting.