Recently, the CoGeNT collaboration reported weakly interacting massive particle 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 LEP experiments, the light CP-even Higgs is favored to be at around 9-10 GeV. Such a scenario can be realized in the ``beyond the minimal supersymmetric standard model'' context. The relic abundance consistent with the WMAP result can be obtained when twice 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 5-6 GeV.