Yb/YAG single crystals were grown from the melt composition of Y_1-xYb_x)₃Al₅O₁₂ where x equal to 5, 10, 15, 20, 25, 33, 50, 75 and 100 at % by floating zone method. Optimum growth parameters to get high quality single crystals were 3.5 mm/h of growth rate and 20 rpm of rotation rate under the N₂ atmosphere. After the growth, color of crystals was appeared with pale blue due to the lack of oxygen, but it was disappeared after annealing at 1450℃ for 2 hr. Absorption coefficients were linearly increased depending on the concentration of Yb³⁺ ions. Broad emission band was measured in the range of 1020 to 1050 nm with the peak intensity at 1031 nm and 1051 nm because of ²F₅2/(1)→²F₇2/(3) and ²F₅2/(1)→²F₇2/(4) transition respectively. When Yb³⁺ ions were substituted with high rates, there were tendency to decrease the measured fluorescent lifetime for Yb ions depending on the concentration of Yb³⁺ ions.