The studied MoS2 nanoribbon with Mo (101¯0) edge symmetrically distributed is not stable. For the two stable structures, the center Mo atom should move about 0.3 Å to the right or left direction. The S atoms on Mo (101¯0) edge show different hydrogen adsorption properties and the active sites for the hydrogen evolution reaction have been determined by analyzing the Gibbs free energies. The electronic structures can explain qualitatively the Gibbs free energy values of MoS2 nanoribbon with hydrogen adsorption and the activity for hydrogen evolution reaction.