Hydrogen has been identified as one of the most promising sustainable and clean energy.Developing hy-drogen evolution reaction(HER)catalyst with high activity is essential for satisfying the future require-ments.Considering novel advantages of two-dimensional materials and high catalytic activity of atomic transition metal,in this study,using density functional theory calculation,the HER on single transition-metal(23 different TM atoms)doped phosphorus carbide monolayer(α-PC)has been investigated.The Volmer-Tafel and Volmer-Heyrovsky reaction mechanisms,and the stability of the most promising HER catalyst are also included.The results show that Ir-αPC with high physical and thermal stability has the most optimal value of Gibbs free adsorption energy for H atom.The relationship of d band center and the HER activity shows a volcano-like curve.The calculation of reaction energy barrier indicates that the Volmer-Heyrovsky step is more favorable than the Volmer-Tafel step.