This study investigates the hydrogen evolution reaction (HER) on various crystal surfaces of zinc anodes using first-principles calculations. The research reveals that the HER activity on Zn (002) and (100) surfaces is governed by the Volmer step, while the HER activity on Zn (101), (102), and (103) surfaces is determined by the Tafel step. The generalized coordination number ( $\overline{CN}$ ) of surface Zn atoms is identified as a key descriptor of HER activity. A higher $\overline{CN}$ corresponds to lower HER activity, as seen on the Zn (002) surface, which has a higher $\overline{CN}$ than the other surfaces. The atomically uneven Zn (002) surface exhibits significantly higher HER activity than the flat Zn (002) surface due to the lower $\overline{CN}$ of surface Zn atoms. The $\overline{CN}$ of surface Zn atoms is proposed as a key descriptor of HER activity, and tuning this parameter could be a vital strategy to inhibit HER on the Zn anode surface. The study provides a theoretical basis for understanding HER on the Zn surface and offers insights into strategies to suppress HER on the Zn anode. The findings highlight the importance of surface structure and coordination in determining HER activity, and suggest that achieving a flat Zn (002) surface could be an effective approach to suppress HER. The research also emphasizes the need for further investigation into the relationship between $\overline{CN}$ and HER activity, as well as the potential for using $\overline{CN}$ as a descriptor in the design of Zn anodes for aqueous zinc-ion batteries.This study investigates the hydrogen evolution reaction (HER) on various crystal surfaces of zinc anodes using first-principles calculations. The research reveals that the HER activity on Zn (002) and (100) surfaces is governed by the Volmer step, while the HER activity on Zn (101), (102), and (103) surfaces is determined by the Tafel step. The generalized coordination number ( $\overline{CN}$ ) of surface Zn atoms is identified as a key descriptor of HER activity. A higher $\overline{CN}$ corresponds to lower HER activity, as seen on the Zn (002) surface, which has a higher $\overline{CN}$ than the other surfaces. The atomically uneven Zn (002) surface exhibits significantly higher HER activity than the flat Zn (002) surface due to the lower $\overline{CN}$ of surface Zn atoms. The $\overline{CN}$ of surface Zn atoms is proposed as a key descriptor of HER activity, and tuning this parameter could be a vital strategy to inhibit HER on the Zn anode surface. The study provides a theoretical basis for understanding HER on the Zn surface and offers insights into strategies to suppress HER on the Zn anode. The findings highlight the importance of surface structure and coordination in determining HER activity, and suggest that achieving a flat Zn (002) surface could be an effective approach to suppress HER. The research also emphasizes the need for further investigation into the relationship between $\overline{CN}$ and HER activity, as well as the potential for using $\overline{CN}$ as a descriptor in the design of Zn anodes for aqueous zinc-ion batteries.