Recent studies suggest that binary neutron star ( NS-NS ) mergers robustly produce the heavy r -process nuclei above the atomic mass number A \sim 130 because of their ejecta consisting of almost pure neutrons ( electron fraction of Y _ { \mathrm { e } } < 0.1 ) . However , little production of the lighter r -process nuclei ( A \approx 90 –120 ) conflicts with the spectroscopic results of r -process-enhanced Galactic halo stars . We present , for the first time , the result of nucleosynthesis calculations based on the fully general-relativistic simulation of a NS-NS merger with approximate neutrino transport . It is found that the bulk of the dynamical ejecta are appreciably shock-heated and neutrino-processed , resulting in a wide range of Y _ { \mathrm { e } } ( \approx 0.09 –0.45 ) . The mass-averaged abundance distribution of calculated nucleosynthesis yields is in reasonable agreement with the full-mass range ( A \approx 90 –240 ) of the solar r -process curve . This implies , if our model is representative of such events , that the dynamical ejecta of NS-NS mergers can be the origin of the Galactic r -process nuclei . Our result also shows that the radioactive heating after \sim 1 day from the merging , giving rise to r -process-powered transient emission , is dominated by the \beta -decays of several species close to stability with precisely measured half-lives . This implies that the total radioactive heating rate for such an event can be well constrained within about a factor of two if the ejected material has a solar-like r -process pattern .