Single crystals of Ca2+xY2-xCu5O10 (x = 0, 0.5, 1.0, 1.5 and 1.8) (CYC) have been successfully grown by the traveling-solvent floating-zone (TSFZ) method. The effect of the atmosphere on the growth was studied. The optimum composition of the solvent was also determined. It is shown that the density of the starting feed rod is crucially important for successful crystal growth. The characterization of the crystals by inductively-coupled plasma (ICP) emission spectroscopy, scanning electron microscopy-X-ray energy dispersion spectroscopy (SEM-EDS) and magnetic susceptibility measurement is reported.