In this work, based on the stochastic model, streamer discharge was modeled and simulated within atmospheric pressure air gap. The plasma channels were followed, step by step, from the anode (rod) to the cathode (plane). That shows the streamer discharge bridges the air gap and indicates the minimum breakdown voltage required for a 3 cm atmospheric pressure air gaps as 27.56 kV. The streamer grows randomly in zigzag path and branched in several positions between the two electrodes. The number and positions of branches appeared depending on the applied voltage values. The electric potential and field distributions shown agreement with the streamer growth according to the simulation development time.