Waste energy recovery is crucial for reducing greenhouse gas emissions and alleviating the increasing demand for central power grids. In the paper, theoretical analyses have been carried out on a novel thermoacoustic combined cooling, heating, and power system for simultaneously recovering waste heat and liquefied natural gas cold energy. The system is designed based on acoustic impedance matching between the thermoacoustic and alternator units for maximizing the overall exergy efficiency. The efficiency, cost savings, and emission reductions of the optimal system are investigated. With cold and waste heat temperatures of 130 K and 500 K, the system achieves an overall exergy efficiency of 24.1%, allowing 78.4 MWh of primary fuel energy reduction, and correspondingly, 30.6 tons of CO2 emissions reduction per year. Investigations are further performed on the system parametric sensitivities. A method for adjusting the alternator external electric impedance is proposed to allow for matching piston displacement within design parameters. Besides, comparisons are made with alternative thermoacoustic cogeneration models. The results show that the proposed system can operate effectively for various supply modes, which is promising for adaptation in different applications. Finally, comparisons are drawn with similar existing technologies and future developments are discussed.