In this paper we study the amplitude Nth-power squeezing of radiation fields in the degenerate Raman process by using the modified effective Hamiltonian approach recently suggested by us. We found that if the field is initially in a coherent state it will not get squeezing for any Nth-power; if the field is initially in a squeezed vacuum, it may get Nth-power squeezing. The time evolution of the field fluctuation was discussed. Its dependences on power-order N, mean photon number bar-n, and squeezing angle xi are analyzed.