Stacked Blumlein pulse generators have the advantages of being flexible and compact, however, switch isolation issue hinders its applications. In this paper, an all-solid-state stacked Blumlein pulse generator is designed. A 4-winding common-mode inductor is used for charging the pulse-forming network, supplying driver circuit and isolating high-voltage. Firstly, the principle of isolation is analysed, an isolated trigger assembly containing common mode inductor and synchronous optical trigger is designed, the charging and discharging process of the stacked Blumlein pulse generator is analysed, and a Blumlein pulse forming network based on IGBT switch arrays is designed; secondly, simulation is carried out on the designed Blumlein pulse forming network and stacked Blumlein pulse generator, and 8-winding common mode inductors are used as the pulse forming network to drive the power supply and high voltage isolation device. Ultimately, an 8-stage stacked Blumlein pulse generator experiment was carried out, and a square wave pulse with a voltage of 30.0 kV, a current of 604 A, and a pulse width of 237 ns was obtained on a matched load.