Molecular oxygen (O2) is essential to human beings on the earth.Although elemental oxygen is rather abundant,O2 is rare in the interstellar medium.It was only detected in two galactic and one extra-galactic region.The inconsistency between observations and theoretical studies is a big challenge for astrochemical models.Here we report a two-phase modeling research of molecular oxygen,using the Nautilus gas-grain code.We apply the isothermal cold dense models in the interstellar medium with two typical sets of initial elemental abundances,as well as the warm-up models with various physical conditions.Under cold dense conditions,we find that the timescales for gas-phase CO,O2 and H2O to reach peak values are dependent on the hydrogen density and are shortened when hydrogen density increases.In warm-up models,O2 abundances are in good agreement with observations at temperatures rising after 105 yr.In both isothermal and warm-up models,the steady-state O2 fractional abundance is independent of the hydrogen density,as long as the temperature is high enough (＞30 K),at which O2 is prevented from significant depleting onto grain surface.In addition,low density is preferable for the formation of O2,whether molecular oxygen is under cold conditions or in warm regions.