Yttrium iron garnet (YTG, Y3Fe5O12) single crystals were grown by the laser-heated pedestal growth method. The pulling rates from 0.1 to 2.0 mm/min were found to affect significantly the structure and composition of YIG crystals. The results of X-ray powder diffraction revealed that, with the pulling rate decreasing, the ratio of the primary X-ray diffraction intensity of YIG to that of YIG and YFeO3 increased. For the crystals grown at fast pulling rates, the cellular structures that resulted from constitutional supercooling were observed through an optical microscope. The periodical cellular structures of the crystals grown at a low pulling rate were also observed. The distribution of elements analyzed by mapping showed the Fe-rich solute was rejected to the interface between the cellular structures. The thermal effect on the YIG crystals was that the higher melt temperature resulted in the stronger oscillatory-thermocapillary convection, which forced the crystals to grow at lower pulling rates to avoid the periodical cellular structure. The present results show that slow pulling rates and low melt temperature are advantageous in obtaining high-quality YIG single crystals.