Acoustic impedance matching is critical to the overall performances of a traveling-wave thermoacoustic electric generator. This paper presents an effective approach for matching the acoustic impedances of the thermoacoustic engine and the linear alternators for maximizing the output electric power and thermal-to-electric efficiency. The acoustic impedance characteristics of the engine and the linear alternators are analyzed separately, and the methods for modulating the acoustic impedances are investigated numerically. Specially, two different coupling locations including one at the resonator and the other one at the loop of the thermoacoustic engine are compared. It is found that the imaginary part of the load acoustic impedance should be near zero for a good output performance of the engine at either coupling location. The real part of the optimal acoustic impedance for the coupling location at the resonator is smaller than that for the one at the loop. The acoustic impedance of the linear alternator can be simply and effectively adjusted to the expected range by tuning the operating frequency, load resistance and the electric capacitance. Both the experiments and numerical simulations show that a better matched condition can be achieved when they are coupled at the location at the resonator. Maximum output electric power of 750.4 W and the highest thermal-to-electric efficiency of 0.163 have been achieved. When they are coupled at the loop, the maximum electric power and the thermal-to-electric efficiency become 506.4 W and 0.146 due to the lower quality of the acoustic matching. The acoustic matching approach presented in the paper would be helpful for guiding the designs of thermoacoustic/alternator and compressor/cryocooler systems.