Power and freshwater demand are increasing as populations around the world keep growing. Due to the environmental impact of using fossil fuels and limited resources, using solar thermal in desalination application is a valuable option. In this paper, an innovative new design of low-temperature multi-effect desalination coupled with mechanical vapor compression (LT-MED-MVC) powered by supercritical organic Rankine cycle (SORC) utilizing a low-grade solar heat source using evacuated tube collectors is analyzed. The proposed design has the potential to desalinate water of high salt concentrations or brine with high salinity more than 100,000 ppm or effluent streams from a power plant with low energy consumption and high efficiency when compared to other systems. The performance of the LT-MED-MVC was found to be better than similar systems found in the literature. The specific power consumption for the system is lower than 4 kW h/m3 for seawater feed salinity of 100,000 ppm, 14 forward feed effects, and a recovery rate of 50%. The overall system efficiency is about 14%. The impact of increasing the number of effects, motive steam temperature, pressure of SORC, and salt concentration on the specific power consumption, solar collector area, and the system efficiency are also analyzed.