The lepton polarization asymmetry in the B → e+e- decay, when one of the leptons is polarized, is investigated by using the most general form of the effective Hamiltonian. We find allowed regions for the new scalar Wilson coefficients, assuming that the experimental branching ratio is measured within 10% percent uncertainty. Then using these restrictions to the new coefficients the sensitivity of the lepton polarization asymmetry to them is studied: Moreover, it is observed that there are regions of terms describing the scalar interactions, where lepton polarization asymmetry differs from zero, which can serve as a good test for searching new physics beyond the standard model.