High quality crystals of $YMnO_3$, which is interested in non-volatile memory device application, were grown by the floating zone method. Optimum condition for powder synthesis was established to be $1200^{circ}C$ for 10 hrs and optimum condition for sintering of $YMnO_3$feed-rod was established to be $1500^{circ}C$ for 10hrs respectively. It was found from non-seeded growth experiment that $YMnO_3$crystal was grown preferentially to the [1010] orientation. The $YMnO_3$single crystal, which was grown to the direction of perpendicular to C-axis, was typically 5mm in diameter, 50 mm in length and showed dark-blue color.