The crystal structure and superconductivity of another superconducting phase in the Tl-Ba-Ca-Cu-O system have been studied. This superconducting phase has a zero-resistance temperature of 100.6 K and diamagnetic susceptibility appears at 98.4 K. The ideal chemical formula is Tl₂Ba₂CaCu₂O₈. The crystal structure of this compound was determined by means of X-ray powder diffraction. It belongs to the body-centred tetragonal system with lattice constants a=3.847 AA and c=29.43 AA. Its space group is D_4h¹⁷ (I4/mmm). Each unit cell contains two formula units. 2 Ca²⁺ cations occupy 2(a) equivalent point positions. 4 Ba²⁺, 4 Tl³⁺ and 4 Cu²⁺ cations occupy the same equivalent point positions 4(e) with respective atomic parameters z=0.115, 0.285 and 0.450. 16 O anions occupy 8(g) (z=0.450) and two 4(e) equivalent point positions (z=0.200 and 0.380). The crystal structure of Tl₂Ba₂CaCu₂O₈ is isomorphic with that of Bi₂Sr₂CaCu₂O₈. Comparing it with the structure of Tl₂Ba_2-xCa_1+xCu₃O₉, both of them have the same lattice constant a, but they have different lattice constants c, as the stacking numbers along the c axis are different. The superconducting transition temperature of Tl₂Ba₂CaCu₂O₈ is lower than that of Tl₂Ba_2-xCa_1+xCu₃O₉. The transition temperature T_c is possibly related to the magnitude of c and the Cu²⁺ content in the unit cell.