We present the first attempt to analytically study the nonlinear matter power spectrum for a mixed dark matter model containing neutrinos of total mass ~0.1 eV, based on cosmological perturbation theory. The suppression in the power spectrum amplitudes due to massive neutrinos is enhanced in the weakly nonlinear regime. We demonstrate that, thanks to this enhanced effect, the use of such a nonlinear model may enable a precision of sigma(m(nu,tot)) ~ 0.07 eV in constraining the total neutrino mass for the planned galaxy redshift survey, a factor of 2 improvement compared to the linear regime.