We report a theoretical study of linear and nonlinear susceptibilities of Raman transition in a Λ-type three-level atomic system. In the Raman transition, if t he population of atoms is all prepared in the ground state which interacts with the control light, the linear susceptibility equals zero, while the third-order nonlinear susceptibility does not equal zero. By decreasing the nonradiative dec ay rate γ12 between the two ground states of the atoms, the Kerr no nlinear refractive index for cross-phase modulation can be significantly enhance d.