The electronic and phonon transport properties of graphene-like boron phosphide (BP), boron arsenide (BAs), and boron antimonide (BSb) monolayers are investigated using first-principles calculations and Boltzmann theory. By considering both the phonon-phonon and electron-phonon scatterings, we demonstrate that the strong bond anharmonicity in the BAs and BSb monolayers can dramatically suppress the phonon relaxation time but hardly affects that of electrons. As a consequence, both systems exhibit comparable power factors with that of the BP monolayer but much lower lattice thermal conductivities. Accordingly, a maximum ZT values above 3.0 can be achieved in both BAs and BSb monolayers at optimized carrier concentrations. Interestingly, very similar p-and n-type thermoelectric performance is observed in the BSb monolayer along the armchair direction, which is of vital importance in the fabrication of thermoelectric modules with comparable efficiencies.