We have developed a novel ion conductor comprising magnesium hafnium tungstate (MgHf(WO4)(3)) as a solid electrolyte for future metal-air batteries. The conductivity of this material measured as 2.5 x 10(-4) S/cm at 600 degrees C is about one order of magnitude higher than that of existing ion conductor with similar structure, such as Sc-2(WO4)(3). We have also elucidated for the first time that MgHf(WO4)(3) has an intrinsic crystal structure, forming one-dimensional (1-D) alignments of individual Mg2+ and Hf4+ ions alternating within quasi-layered WO42- units at Sc3+ sites in Sc-2(WO4)(3). The structure observed by HAADF-STEM clearly coincides with the results obtained by first principle calculation. The mechanism for high ion conductivity is discussed from the viewpoints of its ordered structure and physical property of negative thermal expansion.