Using the universal structure predictor algorithm, we proposed that two-dimensional MnB structures with p4mmm (α-MnB) and pmma (β-MnB) symmetries could be synthesized. This finding was verified by calculating the dynamical stability, molecular dynamics, and mechanical properties. The α-MnB had an in-plane stiffness Y x (=Y y ) around 100 N/m while the β-Mn displayed an asymmetric mechanical stiffness of Y x = 186 N/m and Y y = 139 N/m. Both systems displayed a ferromagnetic ground state with metallic band structures. The calculated magnetic moments were 2.14 and 2.34 µB per Mn-B pair in the α-MnB and β-MnB. Furthermore, we investigated the potential superconductivity. In the α-MnB, we found the unique feature of Kohn anomaly at q~2kF in the diagonal direction of the Brillouin zone. The β-MnB phonon spectra showed a valley of degenerated localized softening vibration modes at the edge of the Brillouin zone. The ZA and LA phonon branches in this valley induced the largest contribution to electron-phonon coupling strength. The calculated total electron-phonon coupling parameters were 1.20 and 0.89 in α-MnB and β-MnB systems. Overall, we predict that the α-MnB and β-MnB systems can display 2D ferromagnetic superconducting states with the estimated critical temperatures of Tc ≈ 10-13 K.