In this article, we present the concept, design, and first implementation of a new solid-state pulse topology: the solid-state impedance-matched Marx generator (IMG). This new topology can bring fast, adjustable pulse generation to a wide range of pulsed power applications. Where the original IMG is a high-power device (using spark gaps) for relatively low-repetition-rate, high-energy-density physics, we require a pulse source with a (sub)nanosecond rise time at moderate voltages of tens of kilovolts at high repetition rates for transient plasma generation. To achieve this, we adapted the IMG pulse source concept to a solid-state concept with additional transmission lines and metal-oxide-semiconductor field-effect transistor (MOSFET) switches. In this article, we present the general concept, a 20-stage design (with 3-D transient electromagnetic simulations), and a first 5-stage, 5-kV prototype. The prototype achieves 5-6-ns rise time pulses at voltages up to 2.5 kV into a matched 50- \Omega load (due to an oscillation in the drive circuit, the pulse was somewhat distorted at higher voltages) and can generate flexible pulse waveforms. Finally, improvements are suggested to achieve the desired pulse specifications.