Recently, in-plane graphene/h-BN (G/h-BN) heterostructure was reported to be the catalytic activity for H₂O₂ synthesis by 2 e^- oxygen reduction reaction (ORR). However, there is rare report for the vertically-stacked G/h-BN heterostructure, which refers to the stacking of graphene domains on the surface of h-BN. Herein, a simulated chemical vapor deposition method was proposed for fabricating abundant vertically-stacked G/h-BN heterostructure by in-situ growing graphene quantum dots (GQDs) on porous h-BN sheets. The catalytic performance of our vertically-stacked heterostructure catalyst is superior to the reported carbon-based electrocatalysts in an alkaline environment, with the H₂O₂ selectivity of 90%-99% in a wide potential range (0.35 V-0.7 V vs. RHE), over 90% faradaic efficiency and high mass activity of 1167 mmolgcatalyst^-1 h^-1. The experimental results and density functional theory simulation verifies that the vertically-stacked heterostructure possesses greatly catalytic performance for 2 e^- ORR and the edge B atoms in the B-centered AB stacking model are the most active catalytic sites. This research well demonstrates the promising catalytic activity for the vertically-stacked G/h-BN heterostructure and provide a facile route for fabricating other vertically-stacked heterostructures.