  Recently, the CoGeNT collaboration reported the WIMP candidate signal events
exceeding the known backgrounds where the light WIMP with large cross section
is supported. Motivated by this issue, we analyze a light neutralino dark
matter scenario with a very light CP-even Higgs mediation in the elastic
scattering process, which provides the mass and direct detection cross section
to explain the CoGeNT result. To be compatible with the result of other
experiments such as LEP and B-factories, the light CP-even Higgs is favored to
be in 9 to 10 GeV. Such a scenario can be realized in the "Beyond the MSSM"
context. The relic abundance consistent with the WMAP result can be obtained
when twice of neutralino mass is close to the light Higgs mass via the
resonance enhancement of the annihilation cross section. As a result, the
neutralino mass is predicted to be at around 5 to 6 GeV.
