Binary neutron star mergers ( BNSMs ) is currently the most promising source of r -process thanks to the detection of GW170817 . The estimated occurring frequency and the amount of mass ejected per merger indicate that BNSMs by itself can account for all the r -process enrichment in the Galaxy . However , the decreasing trend of [ Eu/Fe ] vs [ Fe/H ] of disk stars for [ Fe/H ] \gtrsim - 1 in the solar neighborhood is inconsistent with the flat trend expected from BNSMs with a standard delay time distribution ( DTD ) \propto t ^ { -1 } . This has led to the suggestion that either additional sources or modification to the DTD of BNSMs is required to match the observations . We investigate the effects of natal kicks received during the birth of neutron star binaries on the chemical evolution of r -process element Eu in the Milky Way by combining the results from the galactic dynamics code galpy with a one-zone Galactic chemical evolution model omega . We show that when key inputs from simulations of the inside-out disk evolution are combined with natal kicks , BNSMs can naturally reproduce the observed decreasing trend of [ Eu/Fe ] with [ Fe/H ] in the solar neighborhood without the need for modification to the DTD or additional r -process sources .