The impedance spectroscopy of non-crystalline ionic Conductors in systems of P2O5-Li2O-LiCl-Al2O3, P2O5-Cul-CuCl, GeO2-Ta2O5-Li2O are studied. The models of equivalent circuit for impedance spectroscopy measurement box of non-crystalline specimen is presented, and the dispersion relations for boundery impedance are obtained under certain conditions, the boundary impedance presented here will transit to the constant phase angle impedance.