Based on the modified effective Hamiltonian for the atom field system, the wave function of the system is derived by means of matrix forms. A feasible scheme is presented to generate the four photon coherent states via far off resonant interaction of a degenerate Λ type three level atom with coherent state cavity field. It is also proved that the superposition states of four photon coherent states with more than four component cannot be generated by using the above same method. That is, the four photon coherent states can remain unchanged in the cavity when the third atom with the same velocity as the second atom is injected into the cavity.