A novel geothermal desalination system is proposed and optimized in terms of maximizing the exergy efficiency and minimizing the total cost rate of the system. The system includes a geothermal steam turbine with a flash chamber, a reverse osmosis unit, and a multi-effect distillation system. First, exergy and economic analyses of the system are performed using Engineering Equation software. Then, an artificial neural network is used to develop a mathematical function linking input design variables and objective functions for this system. Finally, a multi-objective optimization is carried out using a genetic algorithm to determine the optimum solutions. The Utopian method is used to select the favorable solution from the optimal solutions in the Pareto frontier. Also, the distributions of the values of design variables within their allowable ranges are investigated. It is found that the optimum exergy efficiency and total cost rate of the geothermal desalination system are 29.6% and 3410 $/h, respectively. Increasing the seawater salinity and decreasing the intake geothermal water temperature result in an improvement in both exergy efficiency and total cost rate of the system, while variations in the flash pressure and turbine outlet pressure lead to a conflict between the exergy efficiency and the total cost rate of the geothermal desalination system over the range of their variations.