The dynamics of the modulation rogue waves in an inhomogeneous nonlinear optical fiber with the periodic modulation are studied. We find that for different modulation amplitudes and modulation frequencies, the modulation rogue wave solution can be Peregrine comb, rogue wave, or the transition state in between, respectively. In particular, the phase diagram of the three kinds of nonlinear states is given at the modulation amplitude and modulation frequency plane. Moreover, the dynamics characteristics of the Peregrine comb and the rogue wave are discussed on the localized soliton background. It is interesting that the main excitation characteristics of the Peregrine combs and the rogue waves on an infinitely wide plane wave background are well maintained on the soliton background. These results pave the way for exciting and manipulating the rogue waves on a local background.