As the increasing of neutrino energy or matter density, the neutrino oscillation in matter may undergo "vacuum-dominated", "resonance" and "matter-dominated" three different stages successively. Neutrinos endure very different matter effects, and therefore present very different oscillation behaviors in these three different cases. In this talk, we focus on the less discussed matter-dominated case (i.e., $|A^{}_{\rm CC}| \gg |\Delta m^{2}_{31}|$), show that as the matter parameter $|A^{}_{\rm CC}|$ growing larger, the effective mixing matrix in matter $\tilde{V}$ evolves approaching a fixed $3 \times 3$ constant real matrix which is free of CP violation and can be described using only one simple mixing angle $\tilde{\theta}$ which is independent of $A^{}_{\rm CC}$. As for the neutrino oscillation behavior, $\nu^{}_{e}$ decoupled in the matter-dominated case due to its intense charged-current interaction with electrons while a two-flavor oscillation are still presented between $\nu^{}_{\mu}$ and $\nu^{}_{\tau}$. At the end of this talk, we discussed the oscillation probabilities when neutrinos/anti-neutrinos passing through a typical white dwarf to give some embryo thoughts on under what circumstances these studies could be applied and put forward the interesting idea of possible "neutrino lensing" effect.