In a cone beam computed tomography (CBCT), the severity of the cone beam artifacts is increased as the cone angle increases. To reduce the cone beam artifacts, several modified FDK algorithms and compressed sensing based iterative algorithms have been proposed. In this paper, we used two pass algorithm and Gradient-Projection-Barzilai-Borwein (GPBB) algorithm to reduce the cone beam artifacts, and compared their performance using structural similarity (SSIM) index. In two pass algorithm, it is assumed that the cone beam artifacts are mainly caused by extreme-density(ED) objects, and therefore the algorithm reproduces the cone beam artifacts(i.e., error image) produced by ED objects, and then subtract it from the original image. GPBB algorithm is a compressed sensing based iterative algorithm which minimizes an energy function for calculating the gradient projection with the step size determined by the Barzilai- Borwein formulation, therefore it can estimate missing data caused by the cone beam artifacts. To evaluate the performance of two algorithms, we used testing objects consisting of 7 ellipsoids separated along the z direction and cone beam artifacts were generated using 30 degree cone angle. Even though the FDK algorithm produced severe cone beam artifacts with a large cone angle, two pass algorithm reduced the cone beam artifacts with small residual errors caused by inaccuracy of ED objects. In contrast, GPBB algorithm completely removed the cone beam artifacts and restored the original shape of the objects.