Large single crystals of α-NaxCoO2 (x=0.91, 0.92, and 0.93) have been successfully fabricated by using the traveling solvent floating zone method. Details on the crystal growth are discussed. The crystal structures were characterized using powder x-ray diffraction and Rietveld refinement. The magnetic susceptibility measurements show that the magnetic properties depend strongly on x. The compound was found to be antiferromagnetic at TN ≈ 20 K for x=0.91 and x=0.92, and paramagnetic for x=0.93. The in-plane and out-of-plane anisotropies were observed for the x=0.91 crystals. In addition, the derived anisotropic g-factor ratios (gab /gc) from the anisotropic susceptibility along H||ab and H||c decreased significantly as the sodium composition increased from x=0.91 to x=0.93.