In plasma-jet-driven magneto-inertial fusion (PJMIF) systems, a high-voltage nanosecond pulsed power supply is required to drive the plasma gun. Marx bank circuit (MBC) is a good candidate to generate nanosecond pulse with high amplitude, fast rise time, narrow pulse width, and low jitter. However, the fundamental topology and operation principle of a positive nanosecond pulse generator are rarely discussed. In this paper, a comprehensive study on the conduction state of fundamental topology and traditional MBC is presented. Furthermore, an improved positive MBC with auxiliary triggering topology (ATT) is proposed. By changing the switching mode from “overvoltage switching-on” to “triggering switching-on”, the system reliability is improved. The output characteristics under different modified stages, triggering capacitors, and main capacitors are investigated. A 4×4 MBC prototype is implemented with optimized parameters to validate the feasibility of the proposed concept. With spark gap switch load, it can generate a high-voltage pulse with an amplitude of 5.04kV, a rise time of 12.4ns, and an FWHM of 12.6ns.