Hydrogen evolution reaction (HER) has become a key factor affecting the cycling stability of aqueous Zn-ion batteries, while the corresponding fundamental issues involving HER are still unclear. Herein, the reaction mechanisms of HER on various crystalline surfaces have been investigated by first-principle calculations based on density functional theory. It is found that the Volmer step is the rate-limiting step of HER on the Zn (002) and (100) surfaces, while, the reaction rates of HER on the Zn (101), (102) and (103) surfaces are determined by the Tafel step. Moreover, the correlation between HER activity and the generalized coordination number ( $$\overline{CN}$$ ) of Zn at the surfaces has been revealed. The relatively weaker HER activity on Zn (002) surface can be attributed to the higher $$\overline{CN}$$ of surface Zn atom. The atomically uneven Zn (002) surface shows significantly higher HER activity than the flat Zn (002) surface as the $$\overline{CN}$$ of the surface Zn atom is lowered. The $$\overline{CN}$$ of surface Zn atom is proposed as a key descriptor of HER activity. Tuning the $$\overline{CN}$$ of surface Zn atom would be a vital strategy to inhibit HER on the Zn anode surface based on the presented theoretical studies. Furthermore, this work provides a theoretical basis for the in-depth understanding of HER on the Zn surface.