To achieve synchronous driving of multiple SiC MOSFET switches in an all solid-state Marx generator, a drive control circuit based on a pulse transformer was designed. The synchronization of multiple drive signals can affect the output waveform parameters of the Marx generator, thus it is required that the drive signal have the characteristics of fast pulse front and low jitter. According to the driving principle and requirements of SiC MOSFET, the influencing factors of pulse front in SiC MOSFET driving circuit were analyzed, and its related parameters were calculated and simulated for verification. A pulse transformer with 10 primary core piercing stages in series was designed, with 1 turn for the primary and 9 turns for the secondary. The second stage was driven by a 10 stage Marx circuit after passing through a positive and negative pulse signal conditioning circuit. The actual measurement results indicate that the resonant circuit composed of the primary leakage inductance of the pulse transformer and the resonant capacitor in intermittent mode has higher driving power, faster pulse front, and better synchronization. The pulse front of the synchronous driving circuit is 112 ns, the pulse width is adjustable from 1 μs to 10 μs, and the frequency is adjustable from 10 kHz to 25 kHz, which can meet the adjustment requirements of solid-state Marx generator parameters.