Gas spark switches had been applied extensively in the field of pulse power technology on account of the advantages of a simple structure, short breakdown time, and high through-current capability. This paper investigates the streamer breakdown process in a two-electrode switch in a nitrogen environment under atmospheric pressure using a numerical method. First, a two-dimensional fluid simulation was carried out for the streamer generated under the negative and positive trigger voltages, and the difference in the breakdown mechanism in the two modes was analyzed. The study showed that when a negative trigger voltage is applied to the rod electrode, a negative streamer from the cathode to the anode will first be formed, and then a positive streamer from the anode to the cathode will be formed. When a positive trigger voltage is applied to the rod electrode, the streamer propagation mechanism is significantly different from that obtained when a negative voltage is applied. In this case, the breakdown mode is a cathode-directed streamer. Finally, we investigated the effect of circuit parameters on the breakdown process. The time scale of breakdown varies greatly with the capacitance. The significant difference in the breakdown process may come from the charging process of the capacitor. The larger the capacitance is, the slower the charging process will be.