Fe81Ga19 single crystals and polycrystals with different orientations are prepared by zone melting directional solidification. Pole figures show that the deviation degrees between [001] orientation and axis are 12°, 5° and 3°, and the in corresponding axial magnetostrictions parallel to external magnetic field are 254×10-6, 271×10-6 and 291×10-6. The[001]orientation single crystal is determined by back-reflection Laue, and the magnetostriction is 312×10-6. The results reveal the relationship between crystallographic orientation and magnetostriction, and the increase of magnetostrictions with deviation degree decreasing. The deviation degrees between [001]orientation and axis of polycrystals are determined by Electron Backscattered Diffraction to be 18.4°, 15.2° and 14.8°, and thir corresponding magnetostrictions are 180×10-6m, 230×10-6 and 235×10-6.