Atmospheric-pressure plasma jets (APPJs) are widely used in biomedical treatment, surface modification, and sterilization, among others because of their advantages of simple structure, strong chemical activities, nonthermal effects, and convenient handling. In this paper, a nanosecond-pulse power generator based on Marx circuit is proposed. The apparatus consists of a nanosecond-pulse generator with crowbar switch and a needle-ring structure electrode. The nanosecond-pulse generator is modularly designed with ten stages; MOSFETs are used as the main switch and crowbar switch on each stage. A field-programmable gate array is used to generate two-channel trigger pulse signals to control the turn-on or turn-off of switches. The generator can produce repetitive pulses with output voltages of up to 8 kV, pulsewidth of 100-1000 ns, rise time of less than 30 ns, and pulse repetition frequencies of 1 Hz to 1 kHz. The designed nanosecond-pulse generator and the needle-ring structure electrode are used to produce argon plasma jets into open air, and the experiments show that the nanosecond-pulse generator can sustain stable APPJs. This paper lays a foundation for the further exploration of the biomedical effects of APPJs.