We propose a series of planar boron allotropes with honeycomb topology and demonstrate that their band structures exhibit Dirac cones at the K point, the same as graphene. In particular, the Dirac point of one honeycomb boron sheet locates precisely on the Fermi level, rendering it as a topologically equivalent material to graphene. Its Fermi velocity (vf) is 6.05 × 105 m/s, close to that of graphene. Although the freestanding honeycomb B allotropes are higher in energy than α-sheet, our calculations show that a metal substrate can greatly stabilize these new allotropes. They are actually more stable than α-sheet sheet on the Ag(111) surface. Furthermore, we find that the honeycomb borons form low-energy nanoribbons that may open gaps or exhibit strong ferromagnetism at the two edges in contrast to the antiferromagnetic coupling of the graphene nanoribbon edges.