Currently, pulsed adders are used as pulsed voltage sources maturely. However, their use as pulsed current sources is significantly limited due to circuit impedance and the characteristics of power devices. This paper presents a simple yet effective design for a pulsed current source, incorporating a solid-state Marx pulsed adder as the primary power source and an inductor for energy storage. In the pulsed current source, a Marx pulsed adder produces high voltage to charge the inductor. Then, the stored inductance energy is converted to generate current pulses on the load; the amplitude of the pulsed current is unaffected by the load impedance within a certain range. The pulsed current source can be designed as a standard module, and several modules can form a cascade system for producing current pulses with higher voltage. Finally, a pulsed current source was developed, which can produce adjustable current pulses with high voltage. The design principles, control methods and the effects of the distribution parameters are described. The feasibility of the cascade pulsed power system was validated in experiments. Nine modules were connected to generate pulses of current 10 A on a 15 kΩ resistor.