YBa2Cu3C7−x (Y123) single crystals have been grown by the modified pulling method (Solute Rich Liquid Crystal Pulling method, SRL-CP). For further superconductor device application, it is important to establish a technique that enables us to produce larger Y123 single crystals consistently. We have investigated the relationship among the crystal size, the crystal rotation rate, the flow pattern in the melt, and the temperature at the crystal growth interface experimentally. Increase of the crystal diameter and/or the crystal rotation rate increased the strength of the forced convection in the melt, and as a result, the temperature at the crystal growth interface increased. This resulted in a reduction of the crystal growth rate. On the other hand, the forced convection should be kept high enough to prevent floating particles attaching to the growing crystal. Therefore, in order to grow a larger single crystal, it was necessary to control the crystal rotation rate according to the change of the crystal diameter with time. We succeeded in crystal pulling along the c-axis of a relatively large Y123 single crystal which was 17 mm × 17 mm and 8 mm in length.