A method for preparing a TiAl intermetallic compound single crystal material, said TiAl intermetallic compound single crystal material comprising, based on atomic percent, an alloy composition of formula: Ti a Al b Nb c (C, Si) d, wherein 43≤b≤47, 6≤c≤10, a+b+c+d=100, and 0.1≤d≤1, said method comprising the steps of: mixing pure raw materials with a purity of 99.9 % or higher of each substance, wherein raw materials of Al, Ti, C or Si have a purity of 99.999% or higher and neat metal raw material of Nb has a purity of 99.95% or higher, in proportions according to the formula of the alloy composition, and melting the materials into master alloy ingots in a cold crucible electromagnetic induction levitation melting furnace at a vacuum level of 10 -3 Pa or lower, followed by a gravity casting process or a suction casting process, to obtain master alloy rods; cutting the master alloy rods into upper rods and lower rods which are used as raw material rods and seed crystal rods respectively in an optical floating zone directional solidification furnace; controlling the distance between the upper raw material rods and the lower seed crystal rods to 1-5 mm; arranging the raw material rods and the seed crystal rods coaxially and to be perpendicular to the horizontal plane, feeding an inert gas for protection during directional solidification, rotating the upper and lower rods in opposite directions at a relative rotational speed of 10-40 rpm, starting heating to melt the opposite ends of the upper and lower rods, adjusting the positions of the upper and lower rods to allow the opposite ends to gradually approach and be joined to each other, adjusting the power of the equipment and maintaining the temperature for 5-10 min, and then adjusting the growth rate to 2.5-30 mm/h when the surface of the floating zone becomes smooth and the melting is even, so as to start the directional solidification; and after the solidification is completed, reducing the power slowly, and slowly separating the solidified specimens from the remaining feed rod specimens; and subjecting the prepared TiAl alloy single crystal rod to vacuum heat treatment by furnace cooling or air cooling at 1250-1350°C for 12 -24 hrs and then at 900°C for 30 min. mixing pure raw materials with a purity of 99.9 % or higher of each substance, wherein raw materials of Al, Ti, C or Si have a purity of 99.999% or higher and neat metal raw material of Nb has a purity of 99.95% or higher, in proportions according to the formula of the alloy composition, and melting the materials into master alloy ingots in a cold crucible electromagnetic induction levitation melting furnace at a vacuum level of 10 -3 Pa or lower, followed by a gravity casting process or a suction casting process, to obtain master alloy rods; cutting the master alloy rods into upper rods and lower rods which are used as raw material rods and seed crystal rods respectively in an optical floating zone directional solidification furnace; controlling the distance between the upper raw material rods and the lower seed crystal rods to 1-5 mm; arranging the raw material rods and the seed crystal rods coaxially and to be perpendicular to the horizontal plane, feeding an inert gas for protection during directional solidification, rotating the upper and lower rods in opposite directions at a relative rotational speed of 10-40 rpm, starting heating to melt the opposite ends of the upper and lower rods, adjusting the positions of the upper and lower rods to allow the opposite ends to gradually approach and be joined to each other, adjusting the power of the equipment and maintaining the temperature for 5-10 min, and then adjusting the growth rate to 2.5-30 mm/h when the surface of the floating zone becomes smooth and the melting is even, so as to start the directional solidification; and after the solidification is completed, reducing the power slowly, and slowly separating the solidified specimens from the remaining feed rod specimens; and subjecting the prepared TiAl alloy single crystal rod to vacuum heat treatment by furnace cooling or air cooling at 1250-1350°C for 12 -24 hrs and then at 900°C for 30 min.