Among multilevel inverter topologies, asymmetric Cascaded H-Bridge (CHB) inverters have higher output-voltage levels than symmetrical ones. However, asymmetric multilevel inverters need pre-stage isolated and floating DC power sources, which make the system complicated and bulky. This paper is focused on solving the problem by using a single-core (magnetically-coupled) multiple-output forward-flyback converter as the prestage of trinary 27-level asymmetric Multi-Level Inverters (MLI). The forward and flyback converter is driven by a single switch with a controller employing both a PWM duty control and frequency control for continuous conduction mode (CCM) forward output and discontinuous conduction mode (DCM) flyback output respectively. Each output, then, can be regulated independently even though the single switch is used. The proposed system and control method are validated using a 1-kW hardware prototype for the experimental verification.