LaAlO3 Single crystals used as a substrate for thin film depositions of a high temperature oxide su-perconductor YB2Cu3O7 and applied to microwave frequencies were grown by the Traveling Solvent Flati-ing Zone (TSFZ) method and characterized. For the growth of LaAlO3 single crystals polycrystalline fe-edrods were prepared from powder mixture of La2O3 and Al2O3 with a mole ratio of 1:1 calcined at 110$0^{circ}C$ for 3h and sintered at 140$0^{circ}C$ for 4h The growth LaAlO3 crystals was 4-5mm in diameter 30mm in length and dark brown. The growth rate was 2-3mm/h and the rotation speeds were 10rpm for an upper ro-tation and 40 rpm for a lower rotation The growing crystals and the feedrods were counter-rotated. The orientation of the grown single crystals of LaAlO3 was identified to be [111] direction. Dielectric constants were measured to be 30-33 between 100 kHz and 1 MHz in the 30$0^{circ}C$ to 45$0^{circ}C$ temperature range and 102 in a range of 100 kHz at the phase transformation temperature of 522$^{circ}C$ Dielectric losses were calculated to be 1.8$ imes$10-4 at the room temperature and 5.7$ imes$10-3 at the phase transformation temperature. Lattice con-stants of the grown crystlals were determined to be aR=5.3806 $AA$ and $alpha$=60.043$^{circ}$ by the least square method.