  In this work, we investigate the radiative leptonic decays D_(s)^- \to \gamma
\ell \bar\nu (\ell = e, \mu) at tree level within the non-relativistic
consistuent quark model and the effective Lagrangian for the heavy flavor
decays. We find that the contributions for the three Feynman diagrams are all
important. With the full calculation, the decay branching ratios are of the
order of 10^-5 for D_s^- \to \gamma \ell \bar\nu and 10^-6 for D^- \to \gamma
\ell \bar\nu, respectively. These decays can be measured at B factories and
future CLEO-C experiments to determine the decay constants f_D_s and f_D.
