We develop a parallel cosmological hydrodynamic simulation code designed for the study of formation and evolution of cosmological structures. The gravitational force is calculated using the TreePM method and the hydrodynamics is implemented based on the smoothed particle hydrodynamics. The initial displacement and velocity of simulation particles are calculated according to second-order Lagrangian perturbation theory using the power spectra of dark matter and baryonic matter. The initial background temperature is given by Recfast and the temperature uctuations at the initial particle position are assigned according to the adiabatic model. We use a time-limiter scheme over the individual time steps to capture shock-fronts and to ease the time-step tension between the shock and preshock particles. We also include the astrophysical gas processes of radiative heating/cooling, star formation, metal enrichment, and supernova feedback. We test the code in several standard cases such as one-dimensional Riemann problems, Kelvin-Helmholtz, and Sedov blast wave instability. Star formation on the galactic disk is investigated to check whether the Schmidt-Kennicutt relation is properly recovered. We also study global star formation history at different simulation resolutions and compare them with observations.