The artifacts of radial edges are obvious shortcoming of external CT image. In order to suppress the artifacts of the radial edge of external CT images the weighted directional total variation (WDTV) algorithm is used to calculate the local directional differences along the radial and tangential directions, and two weighted parameters are introduced to carry out the weighted sum of these two local directional differences. The WDTV algorithm can better describe the sparsity of external CT image gradient magnitude and effectively improve the quality of reconstructed image. In order to meet the needs of high-noise neutron external CT inspection, different total variation (TV) minimization constraints are applied in certain angle ranges near the radial and tangential directions under the framework of WDTV reconstruction model. In the improved WDTV algorithm, TV minimization plays a more obvious role and has stronger performance of suppressing radial edge artifacts and anti-noise. The results of computer simulation and gear cold neutron experiment show that the improved WDTV reconstruction model can suppress the noise of reconstructed images more effectively and improve the quality of reconstructed images.