Unified Power Flow Controller (UPFC) is an essential device of the energy internet due to its flexible regulating ability on power flow. This paper proposes a topology of a Modular Multilevel Converter (MMC) based UPFC combined with a Solid State Fault Current Limiter (SSFCL). Firstly, working mechanism and mathematical model of the topology are analyzed. Secondly, a modified Nearest Level Modulation (NLM) which can effectively improve the waveform quality of output voltages is proposed. Thirdly, control strategies of the shunt and series sides of MMC-UPFC are proposed based on mathematical model. And then, the control strategy of the SSFCL is proposed when the AC fault occurs. Finally, the effectiveness of topology, modulation method and control strategies are verified by PSCAD/EMTDC simulation models.