The incommensurate modulated crystal structure of the new misfit-layer calcium cobalt oxide (Ca0.85OH)(2 alpha) CoO2 was investigated using a superspace-group formalism with synchrotron X-ray diffraction data. The compound is a kind of composite crystal that consists of two interpenetrating subsystems, [CoO2](infinity) layers containing triangular lattices formed by edge-sharing CoO6 octahedra, separated from each other by [2Ca(0.85)OH](infinity) double-layered rock-salt-type slabs. Both the subsystems are monoclinic lattices with the unit cell parameters, a(1) = 2.8180(4) angstrom, b = 4.8938(6) angstrom, c = 8.810(1) angstrom, alpha(0) = 95.75(3)degrees, and alpha=vertical bar q vertical bar=a(1)/a(2)) = 0.57822(8), viz., a(2) = 4.8736 A, with Z = 2. A possible superspace group is C2/m(alpha 10)s0-C2(1)/m(alpha(-1) 10) for the respective subsystems. The atomic positions deviate from the average positions of the fundamental structure due to the incommensurable periodic interaction between the subsystems. A significant structural modulation was found in the [2Ca(0.85)OH] subsystem, whereas the modulation in the [CoO2 subsystem is less than in [2Ca(0.85)OH], due to the tight bonding of the close-packed CoO6 octahedra. The degree of modulation in the CoO2 layers, i.e., the potential modulation, is almost the same as those of other compounds of the misfit-layer cobalt oxides. Flattened CoO6 octahedra indicate hole doping into the CoO2 layers. The [2Ca(0.85)OH] blocks act as the charge reservoir layers, and the defect Ca ions are presumably the source of the holes.