The spatio-temporal evolution of filamentary discharge in dielectric barrier dis charge at atmospheric pressure is studied. A two-dimensional model was solved wi th uniform initial conditions. The simulation results reveal that the breakdowns take place continuously at different positions and gradually spread all over th e discharge space. It is found that under certain conditions the splitting and u niting of filaments can occur, which has been observed in experiments. The split ting of filaments leads to the generation of new filament and the uniting reduce s the number density of filaments in discharge space. The simulation shows that the charges on barrier surface play a dominant role in determining the global sp atio-temporal evolution of filamentary discharge.