Thermoacoustic electric generator is a novel heat-to-power conversion technology with potential high efficiency and reliability, showing great potential in distributed power generation. In this paper, we conduct time-domain acoustic-electrical analogy investigations on a high-power 4-stage looped traveling-wave thermoacoustic electric generator to shed lights on the system performance. The components of a thermoacoustic system are simplified as an acoustic–electrical analogy model, thus saving computational time. Additionally, the nonlinear effects in the regenerator, heat exchanger and resonance tube are considered in establishing the time-domain equations. Method validation shows a reasonable agreement between experimental and simulated results. Transient evolutions of the oscillating pressure and volume flow rate are firstly given. Investigation is then conducted on onset temperature using different working gases of helium, argon, nitrogen, and neon. The results indicate that when the external resistance reaches 70 Ω, the minimum onset temperature difference of 112 K can be achieved with argon as the working gas. For steady-state characteristics, the influences of electric resistance and heating temperature are explored. It is found that higher heating temperature contributes to larger electric power. A large electric resistance results in a large electric resistance at high heating temperature, while the highest efficiency is achieved with a medium electric resistance. Furthermore, higher heating temperature can lead to more irreversible losses. With helium employed, a maximum electric power of 13.3 kW with thermal-to-electric efficiency of 27.4% is achieved with an electric resistance of 150 Ω and a heating temperature of 950 K, and a highest thermal-to-electric efficiency of 33.5% with electric power of 1.38 kW is obtained when the electric resistance and heating temperature are 90 Ω and 750 K, respectively. This study shows that the proposed method provides a new perspective and an effective method for understanding thermoacoustic electric generator.