In a cone beam computed tomography (CT) system, Feldkamp, Davis, and Kress (FDK) algorithm produces cone beam artifacts due to the missing cone region which has the insufficient object sampling in frequency space. While the total variation minimization based iterative reconstruction (TV-IR) may reduce the cone beam artifacts by filling in the missing cone region, it introduces image blurring or noise increase depending on the regularization parameter. In this work, we propose a method to reduce the cone beam artifacts by optimal combination of FDK and TV-IR images. The method maintains the exactness of FDK using FDK data outside the missing cone region and preserves the benefit of TV-IR in cone beam artifact reduction using TV-IR data inside the missing cone region. For the evaluation, defrise disks phantom and vertical plates phantom were used and the image quality was compared using structural similarity (SSIM) with different regularization parameters of TV-IR. The results show that both TV-IR and the proposed method were effective in cone beam artifacts reduction, but the proposed method provided good image quality regardless of the regularization parameter.