The cavity field spectra for the Jaynes-Cummings model with an additional Kerr-like medium are investigated. It is found that the two peak structure appears when the field state in pure number state initially. The peak space is 2χ and the "center frequency" of the spectrum is far away from the resonance frequency due to the increase of the field intensities. The cavity field spectra will be multi peak structure and the peak number increases quickly with the field intensities when the initial field is in superpositions of number states. The influences of the Kerr effect to the cavity field spectra become marked with the increases of the field intensities.