In this work, we reported a comprehensive first-principles study on the hydrogen evolution reaction (HER) catalytic activity of Cu based core-shell nanoparticles (CSNPs). Cu-55 nanoparticle (NP) and M-x@Cu55-x CSNPs (x = 1, 13) with Fe, Ru, and Os as core components were constructed and their structural parameters, stability, and electronic properties were calculated. We found that there exist competing effects during the binding of H atom on the NP surface. The competing effects between the decreasing of negative charge on surface Cu atoms and the surface expansion resulted from the change of core port size and atoms affect hydrogen adsorption oppositely. Among these CSNPs, Os-13@Cu-42 exhibited the best HER catalytic performance with moderate adsorption for H atoms (E-ads = -0.20 eV), low Gibbs free energies of hydrogen adsorption (Delta G(H) = 0.03 eV) and acceptable reaction barrier for H-2 generation (E-b = 0.32 eV), which makes it highly promising as HER electro-catalyst. (C) 2019 Elsevier Inc. All rights reserved.