Motivated by the recent synthesis of a new polymorph of germanium selenide (γ-GeSe) with a honeycomb lattice and an astonishingly high conductivity (even higher than graphite), here we conduct a study on the hydrogen evolution reaction (HER) electrocatalytic performance and electronic properties of γ-GeSe with respect to the thickness effect from monolayer (1L) to trilayer (3L), along with the defect effect. The band structure of γ-GeSe exhibits a camel's back-like structure near the Γ point, existing for all the layers and in the presence of dilute Se vacancy and surface adsorbate like the Pt atom, and a narrow bandgap ranging from 0.544 eV for 1L to 0.252 eV for 3L. We find that pristine γ-GeSe is electrocatalytically inert for all the layers with an endothermic uptake of hydrogen, as indicated by the calculated Gibbs free energy (ΔG H ). However, upon introduction of Se vacancies and surface Pt adsorbates, the HER performance is enhanced, with the HER activity of 1L γ-GeSe surpassing those of bilayer (2L) and 3L γ-GeSe. Moreover, an increase in defect concentration and thickness leads to a decrease in bandgap, developing semimetallic characteristics. With the absence of a transition element and solely s and p orbitals, semimetallic γ-GeSe is unique and holds great promise as a support for fabricating a single atomic catalyst for HER, and our work offers valuable insights into the rational design of 2D electrocatalysts.