The magnetostrictive and magnetic properties of the melt-spun ribbons of (Tb_(0 33)Fe_(0 67))_(1-x)B_x (x=0, 0.02, 0.05, 0.10 and 0.15) alloys are investigated as a function of the surface velocity of the wheel during melt-quenching, The low field sensitivity of magnetostriction is found to be improved substantially by the addition of B. The saturation magnetostrictioin, however, decreases continuously with increasing B content; for example, the magnetostriction at an applied magnetic field of 8 kOe decreases from 1300 ppm (x=0) to 630 ppm (x=0.15) when the ribbons quenched at an optimum condition are considered. Good low field sensitivity of magnetostriction combined with large magnetostriction is obtained for the ribbons with a nanocrystalline grain structure which is achieved in this work even in the as-spun state. The magnetostrictive and magnetic properties are significantly affected by the formation of an amorphous phase; the saturation magnetostriction and magnetization are reduced but the magnetic softness (the low field sensitivity of magnetostriction and coercive force) is improved. The present results are discussed in terms of the variation of the grain refinement/amorphization with the surface velocity and the B content, and the change of intrinsic magnetic properties with the B addition.