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 PdX₂ (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 PdX₂ nanosheets with low concentrations of X vacancies exhibit favorable hydrogen adsorption free energy (ΔG_H*) values, which is desirable for facilitating the HER. Their HER performance can be greatly enhanced using small external strains, during which ΔG_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 PdX₂ 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.