The existence of a topological Dirac nodal loop is predicted for hydrogenated monolayer boron sheets with a nonsymmorphic symmetry. The three-center two-electron bonds in boron compounds restrict the electronic system to be insulating or semimetallic with a Dirac nodal loop. Two types of electronic structures are distinguished by the Z(2) topological index and confirmed by first-principles total-energy calculations. The topological taxonomy, developed in this research, can be applied to other two-dimensional materials and to seek novel Dirac fermions.