Developing highly active and non-precious-metal single-atom catalysts (SAC) for electrochemical water splitting is of great significance to the development of renewable energy technology in future. Herein, 10 first-row transition-metal (TM, from Sc to Zn) single atoms anchored on a graphyne (GY) nanosheet (TM@GY ) as electrocatalysts for water splitting are explored through computational screening approach. It is found that the single atoms prefer to tightly bind at the acetylenic-ring center of GY. Meanwhile, these TM@GY catalysts show metallic properties or reduced band gap, favoring electron transfer during the electrochemical processes. Moreover, both Co@GY and Mn@GY catalysts present good catalytic performance for hydrogen evolution reaction (HER) with both the acetylenic C and TM atoms being highly active sites. However, only the Co@GY catalyst shows good oxygen evolution reaction (OER) activity with an overpotential of 0.55 V. Thus, Co@GY could serve as a potential bifunctional electrocatalyst for water splitting. Besides, the d-band center of TM atoms on TM@GY can be turned through controlling TM atoms with different d-electron number and be used to predict the OER performance. This work highlights that GY doped with single non-precious-metals can be considered for designing high-active and low-cost bifunctional electrocatalysts for practical electrochemical reactions.