Using fast-rise-time high voltage pulse to trigger the switch is an important method to realize its low jitter operation. Combined with theoretical analysis, simulation results and experimental data, the main factors affecting the output pulse rise time of the pulse-transformer-based trigger source are investigated and a fast-rise-time solid-state trigger pulse generator is developed. Research results in this paper indicate that the key factors affecting the output pulse rise time are the leakage inductance of the pulse transformer, the turn-on speed of the semiconductor switch, and the pulse transformer turn ratio. A huge difference is observed in leakage inductance for different winding types. Among three winding types, the maximum leakage inductance is one order of magnitude greater than the minimum one. By selecting SiC MOSFET with a turn-on time less than 15 ns and using pulse transformer with low leakage inductance (<0.5 μH), a 20.4 ns (10%～90%) fast rise time and 16.5 kV output voltage can be achieved. By controlling the SiC MOSFET drive signal pulse width from 35-55 ns, the peak trigger current can vary from 35 to 55 A. The developed fast-rise-time solid-state trigger pulse generator can reliably trigger the vacuum surface flashover switch.