We have implemented the Smoothed Particle Hydrodynamics (SPH) into the cosmological N-body simulation code. The pre-initial particle distribution is set to follow the glacial conditions and the initial temperature of hydro particles is calculated based on the adiabatic process in the expanding backgrounds. Typical adiabatic SPH equations are adopted and, additionally, non-adiabatic processes such as heating/cooling and supernova explosion are added. We study the effect of star formation criteria on the global star formation rate and compare it with the observations.