An intermediate-coupling variational method is presented to investigate the surface electron states in wurtzite A_xB_1-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 electron, 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 V₀ for the wurtzite Al_xGa_1-xN, Al_xIn_1-xN and In_xGa_1-xN, respectively. The results show that the surface-state levels of electron are reduced with the increasing of the composition x in wurtzite A_xB_1-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 Al_xGa_1-xN and Al_xIn_1-xN increase with the increasing of the composition x. However, in the wurtzite In_xGa_1-xN, the case is contrary. The influence of the e-SO-p interaction on the surface electron states can not be neglected in wurtzite A_xB_1-xN.