We describe the details of crystal growth of Sr2RuO4 by a floating-zone method. The superconducting transition temperature T-c can be controlled by adjustment of crystal growth conditions. By optimizing the growth conditions, crystals with T-c up to 1.50 K have been obtained. In addition, we observed three kinds of two-phase composite structures grown under different conditions. They include (I) a Sr2RuO4-Ru eutectic system, in which lamellae of Ru are embedded in the primary phase of Sr2RuO4, resulting in a remarkable enhancement in T-c by a factor of about 2; (2) epitaxial-like intergrowth of ferromagnetic SrRuO3, on Sr2RuO4; and (3) eutectic growth of Sr2RuO4 and a new insulating phase with the possible composition of Sr3RuO5+delta. (C) 2000 Elsevier Science Ltd. All rights reserved.