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. The001orientation 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 001orientation 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.