Ruby single crystals of 6-7 mm in dialneter and 20-25 mm in length were grown by the xenon-arc type floating zone method using a self-designed FZHY1, Calcination and sintering conditions were investigated and optimum growth conditions were established for controlling the factors such as growth rates, rotation speeds and cooling rates. Also the available energy levels of $Cr^{3+}$ were calculated from transmission data. The growth direction of the crystals was [1010] direction identified by Laue back reflection pattern. The distribution of refractive indices on the wafer of the grown crystals was homogeneous except for the edges of the wafer. The crystals could be used as a laser material with a wavelength of 693 nm and a metastate level.