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). 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.