We present the study of a sample of nine QSO fields , with damped-Ly \alpha ( DLA ) or sub-DLA systems at z \sim 0.6 , observed with the X-Shooter spectrograph at the Very Large Telescope . By suitably positioning the X-Shooter slit based on high spatial resolution images of HST/ACS we are able to detect absorbing galaxies in 7 out of 9 fields ( \sim 78 % success rate ) at impact parameters from 10 to 30 kpc . In 5 out of 7 fields the absorbing galaxies are confirmed via detection of multiple emission lines at the redshift of DLAs where only 1 out of 5 also emits a faint continuum . In 2 out of these 5 fields we detect a second galaxy at the DLA redshift . Extinction corrected star formation rates ( SFR ) of these DLA-galaxies , estimated using their H \alpha fluxes , are in the range 0.3–6.7 M _ { \odot } yr ^ { -1 } . The emission metallicities of these five DLA-galaxies are estimated to be from 0.2 to 0.9 Z _ { \odot } . Based on the Voigt profile fits to absorption lines we find the metallicity of the absorbing neutral gas to be in a range of 0.05–0.6 Z _ { \odot } . The two remaining DLA-galaxies are quiescent galaxies with SFR < 0.4 M _ { \odot } yr ^ { -1 } ( 3 \sigma ) presenting continuum emission but weak or no emission lines . Using X-Shooter spectrum we estimate i-band absolute magnitude of -19.5 \pm 0.2 for both these DLA-galaxies that indicates they are sub-L ^ { \star } galaxies . Comparing our results with that of other surveys in the literature we find a possible redshift evolution of the SFR of DLA-galaxies .