A method for manufacturing a transparent ceramic material, comprising the steps of: (i) molding a source powder into a compact, the source powder consisting essentially of - as a main component, a rare earth oxide consisting of terbium oxide and at least one other rare earth oxide selected from yttrium oxide, scandium oxide, and oxides of lanthanoid elements exclusive of terbium, in a molar fraction of at least 40 mol% terbium oxide with the balance of other rare earth oxide, and - an oxide of at least one element selected from Group 2 elements and Group 4 elements as a sintering aid, wherein the total of said rare earth oxide consisting of terbium oxide and at least one other rare earth oxide is at least 95% by weight of the source powder, and the source powder being obtained by furnishing an aqueous solution containing (a) terbium ions, (b) ions of the at least one rare earth element for said at least one other rare earth oxide, and (c) ions of said least one element selected from Group 2 elements and Group 4 elements, letting components (a), (b) and (c) co-precipitate from the solution, and filtering and heat drying the co-precipitate; (ii) sintering the compact at a sintering temperature T wherein 1,300°C ≤ T ≤ 1,650°C, wherein in the course of heating to the sintering temperature the sintering step includes heating from room temperature at least to a predetermined temperature T1, where 1200°C ≤ T1 ≤ T, at a heating rate of at least 100°C/h, and where T1 < T heating from the temperature T1 at a rate of from 1°C/h to 95°C/h, (iii) hot isostatic pressing the sintered compact at 1,300°C to 1,650°C to form the transparent ceramic material in the form of a complex oxide sintered body represented by the formula: (Tb x R 1-x) 2 O 3 wherein x is a number satisfying 0.4 ≤ x < 1.0 and R is at least one other rare earth element selected from yttrium, scandium, and lanthanoid rare earth elements exclusive of terbium, the sintered body having a crystal grain size of from 0.5 μm to 2 μm, and wherein a specimen 11 mm long made from the sintered body has an overall light transmittance at wavelength 633 nm of at least 80.0% and a diffuse transmittance of not more than 1.6% at wavelength 633 nm. (i) molding a source powder into a compact, the source powder consisting essentially of - as a main component, a rare earth oxide consisting of terbium oxide and at least one other rare earth oxide selected from yttrium oxide, scandium oxide, and oxides of lanthanoid elements exclusive of terbium, in a molar fraction of at least 40 mol% terbium oxide with the balance of other rare earth oxide, and - an oxide of at least one element selected from Group 2 elements and Group 4 elements as a sintering aid, wherein the total of said rare earth oxide consisting of terbium oxide and at least one other rare earth oxide is at least 95% by weight of the source powder, and the source powder being obtained by furnishing an aqueous solution containing (a) terbium ions, (b) ions of the at least one rare earth element for said at least one other rare earth oxide, and (c) ions of said least one element selected from Group 2 elements and Group 4 elements, letting components (a), (b) and (c) co-precipitate from the solution, and filtering and heat drying the co-precipitate; - as a main component, a rare earth oxide consisting of terbium oxide and at least one other rare earth oxide selected from yttrium oxide, scandium oxide, and oxides of lanthanoid elements exclusive of terbium, in a molar fraction of at least 40 mol% terbium oxide with the balance of other rare earth oxide, and - an oxide of at least one element selected from Group 2 elements and Group 4 elements as a sintering aid, (ii) sintering the compact at a sintering temperature T wherein 1,300°C ≤ T ≤ 1,650°C, wherein in the course of heating to the sintering temperature the sintering step includes heating from room temperature at least to a predetermined temperature T1, where 1200°C ≤ T1 ≤ T, at a heating rate of at least 100°C/h, and where T1 < T heating from the temperature T1 at a rate of from 1°C/h to 95°C/h, (iii) hot isostatic pressing the sintered compact at 1,300°C to 1,650°C to form the transparent ceramic material in the form of a complex oxide sintered body represented by the formula: (Tb x R 1-x) 2 O 3 wherein x is a number satisfying 0.4 ≤ x < 1.0 and R is at least one other rare earth element selected from yttrium, scandium, and lanthanoid rare earth elements exclusive of terbium, the sintered body having a crystal grain size of from 0.5 μm to 2 μm, and wherein a specimen 11 mm long made from the sintered body has an overall light transmittance at wavelength 633 nm of at least 80.0% and a diffuse transmittance of not more than 1.6% at wavelength 633 nm.