In proton therapy, the Bragg peak of a proton beam reportedly deteriorates when passing though heterogeneous structures such as human lungs. Previous studies have used heterogeneous random voxel phantoms, in which soft tissues and air are randomly allotted to render the phantoms the same density as human lungs, for conducting Monte Carlo (MC) simulations. However, measurements of these phantoms are complicated owing to their difficult-to-manufacture shape. In the present study, we used Voronoi tessellation to design a phantom that can be manufactured, and prepared a Voronoi lung phantom for which both measurement and MC calculations are possible. Our aim was to evaluate the effectiveness of this phantom as a new lung phantom for investigating proton beam Bragg peak deterioration. For this purpose, we measured and calculated the percentage depth dose and the distal falloff widths (DFW) passing through the phantom. For the 155 MeV beam, the measured and calculated DFW values with the Voronoi lung phantom were 0.40 and 0.39 cm, respectively. For the 200 MeV beam, the measured and calculated DFW values with the Voronoi lung phantom were both 0.48 cm. Our results indicate that both the measurements and MC calculations exhibited high reproducibility with plastinated lung sample from human body in previous studies. We found that better results were obtained using the Voronoi lung phantom than using other previous phantoms. The designed phantom may contribute significantly to the improvement of measurement precision. This study suggests that the Voronoi lung phantom is useful for simulating the effects of the heterogeneous structure of lungs on proton beam deterioration.