In this paper, we fabricated Gallium Nitride (GaN) vertical p-i-n diodes grown on free-standing GaN (FS-GaN) substrates. This homogeneous epitaxy led to thicker GaN epi-layers grown on the FS-GaN substrate, but a high crystalline quality was maintained. The vertical GaN p-i-n diode showed a low specific on-resistance of 0.85 mΩ-cm² and high breakdown voltage (BV) of 2.98 kV. The high breakdown voltage can be attributed to the thick GaN epi-layer and corresponds to the mesa structure. Improvement of the device characteristics by the mesa structure was investigated using device simulations. We proved that a deeper mesa depth is able to decrease the electric field at the bottom of the mesa structure. Furthermore, a smaller mesa bevel angle will assist the BV up to 2.98 kV at a 60° bevel angle. Our approach demonstrates structural optimization of GaN vertical p-i-n diodes is useful to improve the device performance.