Industrial computed tomography (CT) is an effective tool for measuring the dimensional characteristics of lattice structures in additive manufacturing parts. However, currently there is no uniform method to evaluate the dimensional measurement errors of industrial CT. Therefore, in this paper, we first evaluate the dimensional measurement errors of industrial CT using a coordinate measuring machine and a hole plate standard; then, we propose a method for conducting the periodic dimensional measurements of the lattice structure based on contour features. Finally, the effectiveness of the method is verified via an example. The result shows that the maximum permissible error of the industrial CT can reach ±(50+L/400) μm, which meets the current testing requirements. The contour feature extraction method can be applied to measuring the periodic dimensional features of lattice structures.