Superconducting single crystals of La1.85Sr0.15CuO4 have been grown at various temperatures without single crystal seeds by the traveling-solvent floating-zone method. In order to avoid the formation of bubbles during the crystal growth process, a flowing atmosphere of 2 atm oxygen or 1 atm air was applied in different temperature range. It was found that the crystal quality could be improved by raising the growth temperature in a certain range, and the orientation changed from (110) to (100) at higher temperature. X-ray diffraction results showed that the full-width at half-maximum of the best as-prepared crystal was 0.086°. The crystals grown in 2 atm oxygen showed a superconducting transition temperature (Tc) of 37.3 K, while the crystals grown in floating air showed a Tc of about 35 K and it could be improved to 36.5 K by annealing in flowing oxygen.