The rare B-c -> D(s)l(+)l(-) decay is investigated by using the most general model-independent effective Hamiltonian. The general expressions of longitudinal, normal, and transversal polarization asymmetries for l(-) and l(+) and the combined asymmetries of them are found. The dependencies of the branching ratios and polarizations on the new Wilson coefficients are presented. The analysis shows that the branching ratios and the lepton polarization asymmetries are very sensitive to the scalar- and tensor-type interactions. These results will be very useful in searching new physics beyond the standard model.