  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 paper, we focus on the less
discussed matter-dominated case (i.e., $|A^{}_{\rm CC}| \gg |\Delta
m^{2}_{31}|$), study the effective neutrino mass and mixing parameters as well
as neutrino oscillation probabilities in dense matter using the perturbation
theory. We find 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 $\nu^{}_{\tau}$. Numerical analysis
are carried on to help understanding the salient features of neutrino
oscillation in matter as well as testing the validity of those concise
approximate formulas we obtained. At the end of this paper, we make a very bold
comparison of the oscillation behaviors between neutrinos passing through the
Earth and passing through a typical white dwarf to give some embryo thoughts on
under what circumstances these studies will be applied and put forward the
interesting idea of possible "neutrino lensing" effect.
