YBa_2Cu_3O_<7-x>(Y123) single crystal growth was succeeded by the modified pulling method (Solute Rich Liquid Crystal Pulling method; SRL-CP method). A Y123 single crystal could be pulled as a primary phase from the surface of the BaO-CuO flux melt contained in the Y_2O_3 crucible in which Y_2BaCuO_5 (Y211) solid existed at the bottom as a source of solute. The Y123 crystals had twins but no Y211 inclusion. The growth interface morphology of the crystals consisted of spiral steps, wave-like steps and linearmacro steps. After appropriate oxygen annealing, the temperature dependence of the resistivity of the crystal was measured. Along both the c-axis and the ab-plane, the resistivity showed a metal-like behavior and the superconductive critical temperature was about 89 K with about a 2 K transition width. By controlling the crystal rotationrate according to the change of the crystal diameter with time, a large sized Y123 single crystal was obtained which was 17 mm square and 8 mm in height.