The efficiency of supersonic combustion is largely dependent on inlet and injection parameters. Additional energy input is required in some off-design conditions, and nanosecond discharge actuation can be a solution. In the present study, a phenomenological model of a nanosecond-pulsed surface dielectric barrier discharge (NS-SDBD) actuator was developed to analyze the combustion enhancement effect for a supersonic combustor with transverse H2 injection. A seven-reaction H2–air combustion model was adopted for the numerical simulation. Dynamic mode decomposition (DMD) was employed to acquire temperature perturbation in spatial and temporal domains. The results show that the actuator provides additional temperature-increment and species transportation through compression waves. The combustion enhancement effect is mainly attributed to the flow perturbation in the shear layer, which promotes the turbulent diffusion of fuel. Given the same power input, the combustion efficiency at the shockwave reflection point is increased by 17.5%, and the flame height is increased by 15.4% at its maximum.