The generation of electricity in space is a major issue for space exploration, and among the viable alternatives, nuclear power systems appear to present a particularly suitable solution, especially for deep space exploration. Recent developments in thermoacoustic engine and liquid metal magnetohydrodynamic (LMMHD) generator technologies have shown that thermoacoustically-driven LMMHD generators are a promising thermal-to-electrical converter option for space nuclear reactors. In order to improve the power density and capacity of current thermoacoustically-driven LMMHD generators, a novel three-stage looped thermoacoustically-driven LMMHD generator is proposed and investigated in this work. A numerical model of the integrated system including a lumped parameter sub-model for the LMMHD generator is developed and validated. Using this model, the effect of key geometric and operating parameters on the operation and performance of the proposed system are investigated numerically, and acoustic field distributions are presented. The results indicate that when the heat source and sink temperatures are 900 K and 300 K, respectively, a thermal-to-electric efficiency of 27.7% with a total electric power of 4750 W can be obtained at a load factor of 0.92. This work provides guidance for the design of similar systems and contributes to the development of a new thermal-to-electrical conversion technology for space applications.