The spatio-temporal behavior in pattern formation in dielectric barrier discharge system is hard to be studied in the mixed gas of air and argon at high pd product, for the discharge duration of micro-discharge (filament) in streamer mode is very short. In this paper, pattern formation phenomenon in streamer mode in dielectric barrier discharge is studied by optical method. A rich variety of patterns has been observed in streamer discharge mode in the mixed gas of air and argon. It's found that the appearance of these patterns is very sensitive to air concentration and applied voltage. Regular patterns such as hexagon and square structure can be formed in this system when the parameters space is proper. The applied voltage for obtaining the hexagon (or square) pattern increases with increasing air concentration. These regular patterns sometimes drift in a certain direction and sometimes rotate stochastically. The drifting velocity is estimated through dividing the filament trace length by exposure time of the photo. It is found that the drifting velocity increases generally with increasing air concentration and the drifting velocity of hexagon pattern is larger than that of square pattern. The light waveforms from irregular pattern or random walking filaments are un-orderly and stochastic. On the contrary, the light waveforms of regular patterns are very orderly and periodical, only two pulses in each half cycle of the applied voltage. In our experiments, it is also found that the spatial frequency of pattern increases with increasing air concentration.