We have grown underdoped (x = 0.11, 0.12) and optimally doped (x = 0.16) La2-xSrxCuO4 single crystals by the traveling-solvent floating-zone technique. In order to prepare good quality cuprate crystals, we have made much effort to optimize the preparation procedures. For example, we haveadopted the sol-gel route to prepare a highly fine and homogeneous La2-xSrxCuO4 precursor powder for fabricating a very dense ceramic feed rod used for the floating-zone growth, and we have also used quite a slow growth rate. The high quality of the grown crystals has been verified by double-crystal x-ray rocking curves, with the full-width-at-half-maximum being only 113-150 arcseconds, which are the best data reported so far for La2-xSrxCuO4 crystals. The superconducting critical temperatures of the grown crystals are 30, 31 and 38.5 K for x = 0.11, 0.12 and 0.16 samples, respectively, according to magnetic measurements.