The enchanting Dirac fermions in graphene stimulated us to seek other 2D Dirac materials, and boron monolayers may be a good candidate. So far, a number of monolayer boron sheets have been theoretically predicted, and three have been experimentally prepared. However, none of intrinsic sheets possess Dirac electrons near the Fermi level. Herein, by means of density functional theory computations, we identified a new boron monolayer, namely, hr-sB, with two types of Dirac fermions coexisting in the sheet: One type is related to Dirac nodal lines traversing Brillouin zone (BZ) with velocities approaching 106 m/s, and the other is related to tilted semi-Dirac cones with strong anisotropy. This newly predicted boron monolayer consists of hexagon and rhombus stripes. With an exceptional stability comparable to the experimentally achieved boron sheets, it is rather optimistic to grow hr-sB on some suitable substrates such as the Ag (111) surface.