Vertical structure GaN power devices fabricated on freestanding GaN substrates have high potentials in ideally efficient energy conversion systems. This letter describes successful acquisition of high avalanche capabilities for high breakdown voltage GaN p-n junction diodes. We have already reported the high avalanche capability by applying a punch-through structure in p-GaN layer, however; the structure caused a drawback of increase in on-resistance and turn-on voltage. By applying a newly developed two-step mesa structure consisting of the first inner mesa with partially thinned p-GaN layer and the second outer mesa etched to n-GaN drift layer, the high avalanche capabilities with reversible current-voltage characteristics have been realized at high breakdown voltages of 4.7-4.8 kV without sacrificing the forward I-V characteristics. The two-step mesa structure transferred the position of the peak electric field in the p-n junction from the dry-etch damaged second outer mesa to the first mesa covered by the thinned p-GaN layer, which could lead the mild breakdown. The high avalanche capability was obtained with good reproducibility regardless of the anode electrode diameter. This structure can contribute to the construction of robust power systems.