A recently experimental discovered(Cheng et al.,Phys.Rev.Lett.114,117001(2015))of superconductivity on the border of long-range magnetic order in the itinerant-electron helimagnet MnP via the application of high pressure makes MnP the first Mn-based superconductor.In this paper,we carry out first-principles calculations on MnX(X = N,P,As,Sb)and find superconducting critical temperature TC of MnP sharply increases near the critical pressure PC ≈ 8 GPa,which is in good agreement with the experiments.Electron-phonon coupling constant λ and electronic density of states at the Fermi level N(EF)are found to increase with pressure for MnP,which lead to the increase of TC of MnP.Moreover,we also find that the TC of MnAs and MnSb are higher than MnP,implying that the MnAs and MnSb may be the more potential Mn-based superconducting materials.