With extensive first-principles density-functional-theory calculations, we investigate the stability and the atomic and electronic structures of the CrB(2)(0001) and MoB(2)(0001) surfaces, each with two different terminations. It is found that the boron-terminated surface is energetically more favorable over the wide range of thermodynamically allowed chemical potentials than the metal-terminated surface for both CrB(2)(0001) and MoB(2)(0001), suggesting a stable layer of graphene-like boron on the surfaces. Our results also show the similarities and the differences in relaxation and in bonding characteristics between the boron-terminated and metal-terminated surfaces.