The proton conductivity values of the best ZrHEDP sample (P/Zr = 3.0) were around 0.01 S/cm at broad RH condition, 40-95%, and promisingly showed low dependence on RH. However, 0.01 S/cm is not adequate for practical application in PEFC, while Nafion has 0.1 S/cm at 90% RH condition. It is because phosphonic acid groups have a lower dissociation constant of proton than sulfonic acid groups. Therefore, if the pKa of the -PO3H2 is enhanced by some methods (e.g., introducing an electron-withdrawing element), it is possible to obtain the material with low dependence on RH and enough proton conductivity for the PEFC operation.