Two-dimensional (2D) boron sheets have been successfully synthesized in recent experiments,h owever,s ome important issues remain, including the dynamical instability, high energy,and the active surface of the sheets.Inanattempt to stabilize2 Db oron layers,w eh ave used density functional theory and global minimum search with the particle-swarm optimization method to predict four stable 2D boron hydride layers,n amely the C2/m, Pbcm, Cmmm, and Pmmn sheets. The vibrational normal mode calculations reveal all these structures are dynamically stable,i ndicating potential for successful experimental synthesis.T he calculated Youngs modulus indicates ah igh mechanical strength for the C2/m and Pbcm phases.M ost importantly,t he C2/m, Pbcm, and Pmmn structures exhibit Dirac cones with massless Dirac fermions and the Fermi velocities for the Pbcm and Cmmm structures are even higher than that of graphene.T he Cmmm phase is reported as the first discovery of Dirac ring material among boron-based 2D structures.T he unique electronic structure of the 2D boron hydride sheets makes them ideal for nanoelectronics applications.