By the floating zone method with infrared radiation convergence type heater homogeneously $Cr^{3+}$ doped alu-mina single crystal was obtained. And sizx {1010} facets appeared at the surface of [0001] grown crystals. $ZrO_2$ and $HfO_2$ precipitated as secondary phase and were not doped in the crystals. We found that the dist-ribution of the secondary phase which was mainly located at the surface and the peripheral region was closely related to the flow pattern of melt zone.