Fe3Al single crystals grown by a floating zone method were compressed at different orientations to examine the orientation dependence of the pseudoelasticity. D0(3)-ordered Fe-23.0at%Al single crystals with an appropriate heat treatment demonstrated a giant pseudoelasticity, although martensitic transformation never occurs in the crystals. In the crystals, a superpartial dislocation with Burgers vector of 1/4<111> moved individually dragging antiphase boundary (APB). A restoring force due to the APB resulted in a giant pseudoelasticity. The strain recovery during unloading depended strongly on crystal ofientatiom The single crystals oriented for planar slip on (101) plane showed a large strain recovery as much as 5.0%. In contrast, the strain recovery at crystal orientation for easy cross slip or multiple slip was smaller than that for planar slip on (101) plane. The forest dislocations or dislocation debris formed by the interaction between several slips hindered the reversible motion of superpartials with b=1/4<111> in both the anti-twinning and the twinning senses. Moreover, the amount of strain recovery in the twinning sense was larger than that in the anti-twinning sense, suggesting that the pseudoelasticity in Fe3Al crystals was influenced by the asymmetry of core structure of the superpartials with a screw character.