Single-atom catalysts embedded in N-doped graphene have attracted great interest recently, but the hexagonal boron nitride (h-BN) is much less explored as a support. Using first principles density function theory and molecular dynamics, here we investigate the stability of Pt, Au, and Ru single atoms anchored at B and N vacancies on h-BN. We find that Pt and Ru single atoms are much more stable than Au on h-BN. We further examine propane dehydrogenation on these single-atom catalysts and find that Pt1 at the B vacancy in h-BN and Ru1 at the N vacancy in h-BN show excellent activity for propane dehydrogenation, as evidenced by low energy barriers for both dehydrogenation steps. Our work suggests that Pt and Ru single atoms anchored at vacancy sites in h-BN could be promising for propane dehydrogenation.