This paper proposes a square wave pulse adder with truncation function based on the self-triggering technology. The N-type switch and the P-type switch are connected in series to form a special half-bridge structure, which only needs to provide an isolated bipolar signal to control the first-stage charging and discharging switches. All other switches are turned on and off step by step to generate high-voltage square wave pulses. This technology not only greatly simplifies the driving circuit of the pulse adder, but also realizes the truncation function to generate quasi-square wave pulses with fast front and back edges. By using the automatic conduction characteristics of the depleted N-type switch, the self-charging without control is realized, and the insulation level of the drive circuit is significantly improved. A 9-stage power supply prototype is built for experimental verification, and the the experimental results show that a stable repetitive positive square wave pulse is generated on a 10 kΩ resistive load. The voltage amplitude is adjustable from 2.3 kV to 3.6 kV, the pulse width is adjustable from 1 μs to 10 μs, and the frequency is adjustable from 0 kHz to 1 kHz. The front and rear edges are both about 100 ns, and accelerate with the increase of operating voltage. The waveform under 10 kΩ and 3 nF resistance-capacitance series load is still a good square wave pulse, and the front and rear edges of the pulse do not slow down significantly with the resistance load. The compact structure of the pulse adder can help to miniaturize solid-state pulse generators.