We propose a novel metal artifact reduction method based on a fractional-order curvature driven diffusion model for X-ray computed tomography. Our method treats projection data with metal regions as a damaged image and uses the fractional-order curvature-driven diffusion model to recover the lost information caused by the metal region. The numerical scheme for our method is also analyzed. We use the peak signal-to-noise ratio as a reference measure. The simulation results demonstrate that our method achieves better performance than existing projection interpolation methods, including linear interpolation and total variation.