The incommensurately modulated structure of copper telluride Cu3-xTe2(Cu2.91Te2) with modulation wavevector q = 0.397 (1)a* + 1/2c* has been determined by X-ray diffraction at room temperature (974 unique reflections). The lattice parameters of the primitive orthorhombic cell of the average structure are: a = 3.9727 (4), b = 4.0020 (5), c = 6.1066 (3) angstrom, V = 97.1 angstrom3, Z = 2, mu = 304 cm-1 (lambda = 0.7107 angstrom), M(r) = 440.1. The symmetry of the structure is given by the superspace group C111BAR(Pmmn). The final R(F) factor is 0.045. The modulated structure is related to the structure of Ni3+/-xTe2 (Schutte & de Boer (1993). Acta Cryst. B49, 392-398] and, as in the latter compound, the occupation of the octahedral sites by metal atoms varies throughout the range 0 to 1. Different from the nickel telluride structure is the antiphase ordering along c together with a different displacement pattern of the atoms, which can be ascribed to a different interaction strength and a different charge transfer between the metal atom and Te.