The plasma filled dielectric Cerenkov maser considering the effect of the plasma grating has been studied. The plasma grating is formed by the modulation of the strong fields. According to the plasma-grating model, An equivalent model is constructed. The modified dispersion relation has been derived.The numerical results show that when the modulation over the background plasma increases, the operation frequency also increases, however, the growth rate varies slightly. Compared with the calculation results obtained by treating the plasma as uniform fluids, the calculation results with the equivalent model describe the bounded bandwidth of the dielectric oscillator more precisely.