This paper presents a new type of all solid state boost Marx pulse generator (BMPG). On the basis of the classic pulse forming Marx circuit, without changing the voltage level of each voltage module, a new switch is added for the isolated inductor energy storage and recovery, so as to realize the output of high-voltage nanosecond pulses. At the same time, in order to improve the voltage level of the semiconductor switch and break the limitation of the voltage of the single-stage pulse forming circuit, a series-connected SiC MOSFETs with a single external driver is designed. The series switch has a simple structure with few components and is extremely easy to use in a modular high voltage pulse generator. Its theoretical feasibility is verified by mathematical model and circuit simulation, and the 10-stage prototype is built in this paper. Under the condition of input DC voltage of 500 V, it can output 18 kV high voltage pulses of 200 ns-1200 ns, and the gain multiple has reached 36 times.