Under the DFT calculations, we systematically investigate the catalytic activities for hydrogen evolution reaction (HER) of two-dimensional (2D) layered GeP3 systems, viewed as the analogues of phosphorene. Our computed results reveal that the monolayer and few-layered GeP3 systems can exhibit the good HER activity, where both the top sites over Ge and P atoms can serve as the most active sites. The correlative catalytic mechanisms are analyzed in detail. Further, we propose the effective strategy through applying the external strain to enhance the HER activity of these 2D layered GeP3 systems by optimizing the adsorption state of H* (Delta G(H*)) or electronic property. Imposing the compressive strain on the monolayer GeP3 and the tensile strain on the few-layered GeP3 can simultaneously endow them with the optimum Delta G(H*) value and good conductivity, bringing higher HER activity. Moreover, we have also constructed series of new sandwich nanostructures by alternately stacking the monolayer GeP3 and graphene, and all of them can uniformly exhibit the outstanding HER activity, due to the optimum Delta G(H*) value and good conductivity. Obviously, all these fascinating findings can be advantageous for achieving the highly efficient and nonprecious HER electrocatalysts based on the excellent GeP3 nanomaterials in the near future.