A new Modular Multilevel Converter with Interleaved half-bridge Sub-Modules (ISM-MMC) is proposed in this paper. The ISM-MMC exhibits a higher modularity and scalability in terms of current ratings with respect to a conventional MMC, while preserves the typical voltage level adaptiveness. The ISM-MMC brings the known advantages of classical MMC to low-voltage, high-current applications making it a novel candidate for the sector of ultra-fast chargers for all types of electrical vehicles (EV). This advanced topology makes it possible to easily reach charging power of the EV charging system up to 4.5 MW and beyond with low-voltage supply. To operate the new converter, a hybrid modulation scheme that helps to exploit advantages of the interleaving scheme, is implemented, and explained in this paper. It has been verified that the typical MMC control methods are still applicable for ISM-MMC. A comparative study between classical MMC and ISM-MMC configurations in terms of output characteristics and efficiency is also given. Furthermore, it has been demonstrated that the number of ac voltage levels is synthetically multiplied by the number of interleaved half-bridge legs in submodules. Numerical simulations and Hardware-in-the-Loop tests are carried out to demonstrate the feasibility of the proposed topology and implemented modulation scheme.