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Traditional thermoacoustic engines using conduction-driven, sensible heat transfer are unable to utilize low-grade thermal energy efficiently. Recently, it has been demonstrated that a phase-change thermoacoustic engine can initiate oscillations at a very low temperature difference; however, the steady-stage performance has yet to be extensively studied. In this work, a phase-change thermoacoustic engine with a looped resonator was simulated, based on a linear phase-change thermoacoustic theory. A binary gas mixture consisting of an inert gas and a condensable component was adopted as the working fluid. We numerically investigated the distributions of pressure, volumetric velocity, and acoustic power in the system. We also examined the steady-state performance (characterized by the pressure amplitude, acoustic power, and thermal efficiency) of the system under different mean pressures and temperature differences. The results show that the phase-change thermoacoustic engine can be driven by very low temperature differences (< 50 K) much more efficiently than its dry equivalent (i.e., the same system but without the condensable component). The findings demonstrate the promising potential of generating acoustic power through low-grade heat recovery, which can then be converted into electricity and cooling.