In an SU(2) spontaneously broken gauge theory with a Higgs triplet, the mass effect of an isospin-1/2 fermion on the fermion-monopole bound states is discussed. It is shown that when the direct coupling between fermion and Higgs field approaches zero, but the Dirac mass is kept finite, then the necessary condition of the fermion-monopole bound state is not satisfied. This result means that the Rubakov effect is absent for SU(2) monopole because of the Dirac mass.