As an important family of 2D materials, MXenes show great potential in various applications due to their specific physical and chemical properties, such as high conductivity and surface activity. Here, we investigate 54 phosphorus-functionalized MXenes (P-MXenes) and screen out 10 stable structures by analyzing their dynamical, thermal, and mechanical stabilities based on first-principles calculations. We find that these stable P-MXenes remain metallic and show weak magnetism. We show that they are effective as electrocatalysts for the hydrogen evolution reaction (HER) with near-zero Gibbs free energies of hydrogen adsorption, which are comparable to that of Pt. To understand the microkinetic process in the HER, an explicit water model is used to examine the Volmer-Heyrovsky (V-H) and Volmer-Tafel (V-T) pathways. We find that P-MXenes show a high HER performance along the V-H process due to the low activation barrier. Our systematic study confirms the possibility for the phosphorus-functionalization of MXenes, guides the design of novel electrocatalysts for the HER via surface-modification, and provides deep understanding on the HER mechanism.