A nanosecond pulse generator with alternating output voltage polarity is developed, and the study of plasma generated by bipolar nanosecond pulse discharge is carried out. The generator first cuts DC voltage into a voltage pulse through solid-state switches IGBT, and uses a saturable pulse transformer to boost the voltage and shorten the pulse rising edge. The generator can output two pulses with opposite polarities in one cycle, and the timing can be flexibly controlled. By choosing devices with proper parameters, two bipolar nanosecond pulse generators with optimized output parameters are developed: ① The peak voltage is 10 kV, and the pulse repetition frequency in burst mode is 500 kHz (interval between positive and negative pulses is 2 μs), with continuous repetition frequency of 1 kHz; ② The peak voltage is 25 kV, with 200 kHz burst frequency, and the continuous frequency is 600 Hz. The operating performance of the generators is tested, and it is found that the temperature of the generators tends to increase to a stable point during long-duration(more than half an hour) operation. When the 10 kV generator continuously works at 1 kHz, its highest temperature is 50.5 ℃. For the 25 kV generator continuously working at 600 Hz, the highest temperature point is 60 ℃. The result of using the generators to drive the wire-to-plate electrode and the surface dielectric barrier discharge proves that the generators can be used to generate large-area plasma in atmospheric air.