An intermediate-coupling variational method is presented to investigate the surface electron states in wurtzite AxB1-xN(A,B=Al,Ga and In)ternary mixed crystals(TMCs).Corresponding effective Hamiltonian are derived by considering the surface-optical-phonon(SO-phonon)influence and anisotropic structural effect.The surface-state energies of elec-tron,the coupling constants and the average penetrating depths of the electronic surface-state wave functions have been numerical computed as a function of the composition x and the surface potential Vo for the wurtzite AlxGa1-xN,AlxIn1-xN and InxGa1-xN,respectively.The results show that the surface-state levels of electron are reduced with the increasing of the composition x in wurtzite AxBi-xN.It is also found that the electron-surface-optical-phonon(e-SO-p)coupling lowers the surface-state energies of electron and the shifts of the electronic surface-state energy level in the wurtzite AlxGa1-xN and AlxIn1-xN increase with the increasing of the composition x.However,in the wurtzite InxGa1-xN,the case is contrary.The influence of the e-SO-p interaction on the surface electron states can not be neglected in wurtzite AxB1-xN.