In this study, the energetic and exergetic analysis of a multi-effect desalination system with a thermal vapor compression desalination system has been numerically evaluated. For this purpose, the mass, energy, and exergy balance equations for the thermo-compressor, first effect as well as middle effects, and condenser have been developed. The effects of motive steam pressure and number of effects on yield, gained output ratio (GOR), performance ratio (PR) and irreversibility have been examined. Nanoparticles were used to improve the heat transfer properties at different stages. The highest rate of exergy destruction with 61.67% is concerned with thermo-compressor, owing to the large difference between the motive steam pressure and the entrained steam. The lowest exergy losses rate among the various components was 4.89% for the condenser, due to the fact that much of the final distillate steam entrained the thermo-compressor. As the number of effects increased from 1 to 7, the yield, GOR as well as PR, improved by approximately 590% and the irreversibility reduced by 1.88%. As the motive steam pressure increased from 400 to 1290 kPa, the yield decreased by 25.45% while the GOR and PR improved by 12.62 and 14.8%, respectively. From the second law viewpoint, irreversibility intensified by 16.11% which in turn diminished the second efficiency by 3.17%.