Desalination can provide additional water resources in water‐stressed zones and also in zones suffering from water pollution or insufficient/overexploited groundwater. This study carried out the energy and exergy assessments of a multi‐effect desalination unit driven by a gas turbine based on the specific exergy cost (SPECO) approach. The chemical exergies of brine and seawater are explicitly considered (most studies consider the same specific heat for input seawater and output brine). In addition, the enthalpy of each flow of the desalination unit is considered according to its salt concentration (results are then compared to the constant specific heat model). The highest exergy rates of fuel and product are obtained at the combustion chamber, and its exergy efficiency is 67.83%. The lowest exergy efficiencies were obtained at the condenser, followed by the first effect of the desalination unit, and the heat recovery steam generator. The overall exergy efficiency of the multi‐effect distillation unit is 21.49%. Regarding exergy destruction, as expected, the highest rate was obtained at the combustion chamber, which contributed with 41% to the overall exergy destruction, followed by the regenerator and heat recovery steam generator, with contributions of 16% and 11%, respectively, to overall exergy destruction.