We present the results of a numerical study on the effects of metal enrichment and metal cooling on galaxy formation and cosmic star formation (SF) history using cosmological hydrodynamic simulations. We find following differences in the simulation with metal cooling when compared to the run without it: (1) the cosmic star formation rate (SFR) is enhanced by about 50 & 20% at z=1 & 3, respectively; (2) the gas mass fraction in galaxies is lower; (3) the total baryonic mass function (gas + star) at z=3 does not differ significantly, but shows an increase in the number of relatively massive galaxies at z=1; (4) the baryonic mass fraction of intergalactic medium (IGM) is reduced at z<3 due to more efficient cooling and gas accretion onto galaxies. Our results suggest that the metal cooling enhances the galaxy growth by two different mechanisms: (1) increase of SF efficiency in the local interstellar medium (ISM), and (2) increase of IGM accretion onto galaxies. The former process is effective throughout most of the cosmic history, while the latter is effective only at z<3 when the IGM is sufficiently enriched by metals owing to feedback.