In recent years, the share of natural gas in total primary energy consumption has gradually increased around the world. In China, almost half of imported natural gas is in the form of LNG. Thus, how to effectively use LNG’s cold energy or exergy has gained increasing attention. In this paper, a double-acting thermoacoustic Stirling heat electrical generator capable of using LNG cold exergy is introduced. The system consists of a four-unit thermoacoustic Stirling engines and four linear alternators connected end-to-end to construct a loop configuration. The engine converts the external thermal energy to acoustic work by completing the thermoacoustic Stirling cycle between the low temperature provided by the LNG and that of the ambient environment. Then, the alternator converts the acoustic work to electrical power. To understand the system’s operating mechanism, numerical simulation is performed based on the classic thermoacoustic theory. Besides the distributions of key parameters, the influences of the electrical parameters on the system performance and the optimization of the regenerator in low temperature are presented in detail. According to the simulation results, the regenerator of the engine prefers a higher porosity to achieve high power and efficiency. The maximum acoustic work of 17.6 kW and electrical power of 12.4 kW for the whole system is obtained with a porosity of 0.9 and a hydraulic radius of 53 μm when the electrical resistance and capacitance are 160 Ω and 80 μF, respectively. The cooling and heating temperatures are 110 K and 303 K. This study presents a new way to efficiently use the cold exergy of LNG and may be especially relevant for distributed small-scale applications.