In order to overcome the limitations of the existing classical and solid-state Marx pulse generators, this paper proposes a new modular multilevel voltage-boosting Marx pulse generator (BMPG). The proposed BMPG has hardware features that allow modularity, redundancy, and scalability as well as operational features that alleviate the need of series-connected switches and allows generation of a wide range of pulse waveforms. In the BMPG, a controllable, low-voltage input boost converter supplies, via directing/blocking (D/B) diodes, two arms of a series modular multilevel converter half-bridge sub-modules (HB-SMs). At start up, all the arm's SM capacitors are resonantly charged in parallel from 0 V, simultaneously via directing diodes, to a voltage in excess of the source voltage. After the first pulse delivery, the energy of the SM capacitors decreases due to the generated pulse. Then, for continuous operation without fully discharging the SM capacitors or having a large voltage droop as in the available Marx generators, the SM capacitors are continuously recharged in parallel, to the desired boosted voltage level. Because all SMs are parallelly connected, the boost converter duty ratio is controlled by a single voltage measurement at the output terminals of the boost converter. Due to the proposed SMs structure and the utilization of D/B diodes, each SM capacitor is effectively controlled individually without requiring a voltage sensor across each SM capacitor. Generation of the commonly used pulse waveforms in electroporation applications is possible, while assuring balanced capacitors, hence SM voltages. The proposed BMPG has several topological variations such as utilizing a buck-boost converter at the input stage and replacing the HB-SM with full-bridge SMs. The proposed BMPG topology is assessed by simulation and scaled-down proof-of-concept experimentation to explore its viability for electroporation applications.