Adsorption of hydrogen molecules onto the pristine MoSe2 monolayer and N-, P-, Ru-, Rh-, Os- and Ir-doped MoSe2 monolayer surfaces was investigated using periodic DFT method. Adsorption abilities of the pristine and MoSe2 doping derivatives on hydrogen molecule adsorptions are in order: Os-MoSe2 ( Delta E-ads = -2.19 eV) > Ru-MoSe2 ( Delta E-ads = -1.54 eV) > Ir-MoSe2 ( Delta E-ads = -1.08 eV) > Rh-MoSe2 ( Delta E-ads = -0.63 eV) > N-MoSe2 ( Delta E-ads = -0.22 eV) > P-MoSe2 ( Delta E-ads = -0.15 eV) > pristine MoSe2 ( Delta E (ads) = -0.06 eV). The adsorption energy of hydrogen onto the Os-MoSe2 surface, which is the most active derivative, stronger than the second most active, the Ru-MoSe2 by 0.65 eV (42%) was found. Nevertheless, all the MoSe2 doping derivatives utilized as hydrogen storage for energy storage purposes were suggested.