The Marx circuit structure based on fast high-power semiconductor devices is the classical way of generating picosecond pulses. However, most reported studies suggest that as the number of stages in the Marx circuit increases, the output pulse amplitude tends to saturate. This has of late made high-voltage picosecond-pulse generation a challenge. In this paper, as the number of stages increases, the internal resistance of the avalanche transistor tends to decrease with increasing current flowing through the avalanche transistor. A step-by-step wiring and debugging of the avalanche transistor-based Marx circuit demonstrates this experimentally. That is, for a certain range in the number of stages, saturation of the output pulse amplitude for the Marx circuit of avalanche transistors is not apparent. Introducing a parallel structure for the transistors not only increases the current level of the entire circuit but also further reduces the equivalent resistance of the avalanche transistors, thereby improving the output efficiency. Drawing on microstrip transmission theory, and combining the Marx circuit and avalanche transistor parallel structure, component parameters and circuit topology of the picosecond-pulse generator were redesigned, and a 30-level Marx circuit with a parallel structure of two avalanche transistors was developed. The picosecond-pulse generator outputs a pulse with adjustable voltage amplitude of 0.9–3.1 kV, a 350-ps full-width at half-maximum, a 150-ps rise time, and an adjustable high-stability repetition rate of up to 10 kHz. The number of pulses is precisely controlled. The generator is an all-solid-state compact device with high frequency suitable for research needs.