Crystals of the quaternary compounds α-Lu(Al1-xTx)B4 (T = Fe, Cr) (YCrB4-type, orthorhombic, Pbam), obtained from the nominal composition of Lu(Al1-xTx)B3, were grown by using Al flux mixed with T metal at 1773 K for 5 h under an Ar atmosphere. The maximum dimensions and morphology of the crystals obtained were about 0.7 mm × 0.5 mm for flake-type crystals of Lu(Al1-xCrx)B4 and about 5.2 mm × 0.2 mm for prism crystals of Lu(Al1-xFex)B4 . The lattice constants determination and chemical analyses of Lu(Al1-xTx)B4 (T = Fe, Cr) compounds were carried out for Fe 0.5-10.0 at% and Cr 0.5-1.0 at%. The lattice constants and the unit lattice volume in Lu(Al1-xTx)B4 crystals decreased with increase of the concentration of Fe or Cr. The values of micro-Vickers hardness of Lu(Al1-xFex)B4 (x = 0.005-0.030) and Lu(Al1-xCrx)B4 (x = 0.005-0.010) samples are in the ranges of 16(2)-20(3) GPa and 13(2)-16(3) GPa, respectively. The hardness values showed a little increase as the solid solution of Fe or Cr was realized in Lu(Al1-xTx)B4, possibly because of distortion to the crystal structure. The magnetic susceptibility of as-grown Lu(Al0.995 Fe0.005 )B4 crystals for example, exhibited diamagnetic behavior with a small ferromagnetic component.