Two-dimensional transition metal dichalcogenides (TMDs) have emerged as promising catalysts for the hydrogen evolution reaction (HER). However, they typically require the engineering of additional actives sites ( e.g. vacancies and dopants) and/or the application of large external strains to launch the HER on their basal planes. Herein, we investigate the HER proceeding on the experimentally available single-layer PdX 2 (X = S, Se), a novel group of pentagonal TMDs with high amounts of intrinsic X vacancies, through density functional theory computations. Our results indicate that single-layer PdX 2 nanosheets with low concentrations of X vacancies exhibit favorable hydrogen adsorption free energy (Δ G H* ) values, which is desirable for facilitating the HER. Their HER performance can be greatly enhanced using small external strains, during which Δ G H* can reach the optimal value of 0 eV. Moreover, a kinetic analysis based on the explicit water model and charge extrapolation scheme demonstrates that the HER occurs on the PdX 2 nanosheets according to the Volmer-Tafel mechanism with low energy barriers. This work highlights the realization of high HER activity on TMDs featuring unique structural characteristics.