Considering the three transport mechanisms of diffusion, drift and the photovoltaic effect, we set up a set of coupling differential equations that describe the dynamics of the two-color holographic storage in doubly doped LiNbO3:Fe:Mn in the case of small signal and modulation, and solve the equations to explain the time dynamic development process of holographic storage by using the numerical calculation method. On the basis of these results, we analyze the effect of oxidation-reduction on the process of holographic storage, the non-volatile holographic storage is realized only if the sum Na of number density of the acceptors (Fe3+ and Mn3+) is larger than the number density of iron ions N2. Diffraction efficiency of fixed grating increases with oxidation, photorefractive sensitivity decreases with oxidation, higher diffraction efficiency is at the cost of lower photorefractive sensitivity. When the concentration of doped iron is constant, the higher the concentration of doped manganese, the larger the effective dynamic range of state of oxidation-reduction is, in which holograph can be saved permanently.