Single crystals of $RAI_3(BO_3)_4$ (R=Y, Nd and Gd) were grown by top-seeded solution growth. For the growth of $RAI_3(BO_3)_4$(RAB) single crystals, vairous flux systems of $K_{2}O$, $MoO_{3}$, BaO and $B_{2}O_{3}$ were used. The effects of the cooling rate, rotation speed and seed orientation on the quality and morphology of the grown crystals were investigated. Large single crystals in size of 20mm could be grown at a cooling rate below $2.4^{circ}C/day$ and rotation speed of 30~40rpm. The quality and morphology of RAB crystals seemed to strongly dependent on these growth conditions. The space group of $NdAI_{3}(BO_{3})_{4}$ crystal was confirmed to be C2/c whereas the space group of $YAI_{3}(BO_{3})_{4}$ and $GdAI_{3}(BO_{3})_{4}$ are R32. The phases diagram of $NdAI_{3}(BO_3)_{4}$ - $YAl_{3}(BO_{3})_{4}$ system was determined by x-ray powder diffration and DTA analysis. Optical properties and Nd content in NYAB crystal were studied.