The cavity field spectrum of a pair of two-level atoms interacting with single-mode field with different coupling constants is studied. The new properties of the spectrum structure are discussed when the fields are initially in various number states. It is found that the shifts of peak-positions are symmetrical with the increase of R from 0 to 1. With the increase of R, the number of the Rabi peaks changes according to 2→6→4 when the field is vacuum initially; and the peak number changes according to 2→6→12→9→7 for weak initial fields; the peak number changes according to 2→8→11→5 for strong fields. The peak-height changes rapid when the increase of R is from 0 to 0.3 for vacuum field, from 0 to 0.5 for weak field, and from 0 to 0.1 for strong field. When the photon-number of the initial field is vary large, the peak number changes according to 3→5→3 with the increase of R. The total height of the peaks increases monotonously with R changing from 0 to 1. The cooperative effect of atoms was shown.