Texture of wire of Ti-24mok%Nb-3mol%Al biomedical shape memory alloy was investigated by electron backscatter diffraction pattern (EBSP) and X-ray diffraction (XRD) analysis. The alloy is parent β(bcc) phase at room temperature and exhibits superelasticity. An ingot was fabricated by Ar arc-melting and homogenized at 1273K for 7.2ks in vacuum and then quenched into water. The ingot was cold-drawn with a reduction in cross-section about 90% and a wire with a cross-sectional diameter of 1mm was successfully obtained. The solution-treatments at 873K, 973K, 1073K, and 1173K for 3.6ks were made to evaluate the effect of annealing temperature on the recrystallization texture. The fiber texture of <102>_β was formed in the wire which was solution-treated at 873K and as-rolled one. The texture was broaden and approached to the <110>_β fiber texture with the increase in the solution-treatment temperature. The wire is used in a bending mode in the practical use and superelastic deformation in tension and compression along the wire-direction is necessary. The maximum transformation strains of the β-α"(C-orthorhombic) thermoelastic martensitic transformation are +2.6% and -2.1% along <102>_β whereas they are +2.9% and -0.8% in the <110>_β fiber texture. <102>_β texture is, therefore, favorable for the wire material in this alloy.