Yb3+-doped (Lu,Y)AlO3 single crystals have been grown by the micro-pulling-down method with a radio-frequency heating system. Starting melt compositions of LuxY0.9-xYb0.1AlO3 were varied with x=0.1, 0.2, 0.35, and 0.4. The best Yb3+-doped (Lu,Y)AlO3 single crystals were obtained applying a pulling rate of 0.12 mm/min. To investigate the compositional homogeneity, the effective segregation coefficient of Lu and Yb ions was estimated keff=1.02 and 1.05 for Lu0.2Y0.7Yb0.1AlO3 crystal, respectively. Absorption, radio-luminescence and luminescence decay kinetic of Yb3+-doped (Lu,Y)AlO3 was investigated for room temperature conditions and found to be similar to that of Yb3+-doped YAlO3. Very fast charge transfer luminescence of Yb3+ in the near ultraviolet to visible spectral range and the high density of the LuAlO3 make this material a promising candidate for fast scintillators.