NOVELTY - A lithium lanthanum titanium oxide sintered material comprises lanthanum-lithium-titanium trioxide-containing compound, aluminum trioxide including 0.35 wt.% or less aluminum, and silicon dioxide including 0.1 wt.% silicon. The lithium lanthanum titanium oxide sintered material has average particle diameter of 18 mu m or more, frequency of 15-13 MHz measured using impedance analyzer, and lithium ion conductivity of 3.0x 10-4 S/cm or more at 27 degrees C measured using preset relation.    USE - Lithium lanthanum titanium oxide sintered material is used for solid electrolyte for lithium-air battery and all-solid-state lithium ions battery (all claimed). Uses include but are not limited to personal computer, video camera, mobile telephone, and electric vehicle or hybrid vehicle.    ADVANTAGE - The lithium lanthanum titanium oxide sintered material has favorable lithium ion conductivity.    DETAILED DESCRIPTION - A lithium lanthanum titanium oxide sintered material comprises lanthanum-lithium-titanium trioxide-containing compound ((1-a)LaxLi2-3xTiO3-aSrTiO3, (1-a)LaxLi2-3xTiO3-aLa0.5K0.5TiO3, LaxLi2-3xTi1-aMaO3-a and Srx-1.5a-2xTi0.5Ta0.5O3), aluminum trioxide including 0.35 wt.% or less aluminum, and silicon dioxide including 0.1 wt.% silicon, where x is 0.55-0.59, preferably 0.57, a is 0-0.2, preferably less than 0.05 and M is iron and gallium. The lithium lanthanum titanium oxide sintered material and has average particle diameter of 18 mu m or more, frequency of 15-13 MHz measured using impedance analyzer, and lithium ion conductivity of 3.0x 10-4 S/cm or more at 27 degrees C measured using relation: (1/Rb+Rg)x (L/S), where Rb is resistance value of grains in ( Omega ), Rg is resistance value of grain boundary in ( Omega ), L is thickness of lithium lanthanum titanium oxide and S is area of electrode. INDEPENDENT CLAIMS are included for the following:    (1) solid electrolyte;    (2) lithium-air battery (1); and    (3) all-solid-state lithium ion battery.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of the lithium-air battery.    Lithium-air battery (1)    Negative electrode active material layer (3)    Electrolyte solutions (4,6)    Solid electrolyte (5)