The adsorption and dissociation of O2 molecules on W(111) surface have been studied at the density functional theory (DFT) level in conjunction with the projector augmented wave (PAW) method. All passable dissociation reaction paths of O2 molecule on W(111) surface are considered. The nudged elastic band (NEB) method is applied to locate transition states, and minimum energy pathways (MEP). We find that there is an existing of little barriers for the dissociations reaction of O2 molecule. Ab initio molecular dynamics simulation is also preformed to study the adsorption and dissociation mechanism of O2 molecules on the W(111) surface. Our results indicate that O2 molecule will be dissociated by inclined deposition at temperature of 10 K, but can stable adsorb on top site by normal deposition. The change of bond length and adsorption energy in process of dissociation of O2 molecules on the W(111) surface are also calculated. The O2 coverage effect is also discussed in this paper.