In a cone-beam computed tomography (CT) system, the Feldkamp, Davis, and Kress (FDK) algorithm produces cone-beam artifacts due to insufficient object sampling in the missing cone region of frequency space. While total variation minimization-based iterative reconstruction (TV-IR) may reduce cone-beam artifacts by filling in the missing cone region, it introduces image blurring or noise increase depending on the regularization parameter. In this paper, we propose a method to reduce cone-beam artifacts through an optimal combination of FDK and TV-IR images. The method utilizes FDK (TV-IR) data outside (inside) the missing cone region, which enables to keep the original image quality of the FDK image and preserve the advantages of the TV-IR image for cone-beam artifact reduction. To validate the proposed method, we used numerical phantoms composed of Defrise disks, vertical plates, and star objects and assessed the image quality of FDK, TV-IR, and the proposed method using the mean squared error, contrast to noise ratio, and structural similarity with different TV-IR regularization parameters. Experimental validation was also conducted using a spine phantom with a bench-top cone-beam CT system. The results showed that the performance of the cone-beam artifacts reduction in TV-IR depended on the value of the regularization parameter, which often produced suboptimal image quality for different imaging tasks. However, the proposed method provided good image quality regardless of the regularization parameter values.