A large-eddy simulation (LES) model with a new localized dynamic subgrid closure for the magnetohydrodynamics (MHD) equations is used to investigate plasma-assisted combustion in supersonic flow. A 16-species and 74-reactions kinetics model is used to simulate hydrogen-air combustion and high-temperature air dissociation. The numerical model is validated with experimental data for non-reacting and reacting supersonic flow over a rearward-facing step. The creation of a plasma source near the step corner is shown to have a strong localized effect with the high temperature region resulting in an increase of the radical species concentration in the mixing region. This has the potential for enhancing combustion. In addition, downstream fuel–air mixing is improved, primarily by the creation of a strong baroclinic torque effect in the near field of the plasma source. Furthermore, by adding an uniform external magnetic field, the Lorentz force effect helps to further enhance mixing by lifting the shear layer and increasing fuel penetration by approximately 20%.