Some basic observational properties of Damped Lymna α systems (DLAs) have been examined by Monte Carlo simulation based on the assumption that DLAs are disks form at the center of dark halo at redshift 3. We found that the predicted cosmic star formation rate density contributed by DLAs is consistent with the most recent observations if the star formation timescale in DLAs is assumed to be 1 ∼ 3 Gyr. By comparing the UV luminosity function between DLA host galaxies and that of Lyman Break Galaxies(LBGs), we show that the DLAs host galaxies are much fainter than LBGs, and that only few percent of DLAs can host LBGs. The discrepancy between model prediction and observation in the correlation between metallicity and HI column density for DLAs is reproduced on the basis of Kennicutt star formation formalism at high redshift. It is quite difficult to interpret this concerning the complexities of dust depletion, star formation mode as well as model limitations. Further investigations are needed.
