Archimedes screw turbines have gained popularity in generating power from flowing water. One aspect that hasn't been considered yet is optimizing those parameters that are considered assumptions in the prediction models. In this research, a simple procedure was introduced to design an appropriate Archimedes screw turbine for a given site using a prediction model and an optimization model. First, the mathematical efficiency prediction model of Archimedes screw turbines was developed and validated with experimental and real-world Archimedes screw turbine data. Then, the grey wolves optimization algorithm was developed to be used as an actual engineering application, sensitively analyzed, and coupled with the prediction model. The prediction models were evaluated. The model convergence was investigated, and then, the optimization parameters were found to get maximum efficiency. The results revealed that the optimum number of iterations and grey wolves are 200 and five, respectively. Also, the best values for the inner diameter to the outer diameter ratio, the pitch to the outer diameter ratio, tilt angle, and blade number were found in ranges: 0.43–0.56, 1–1.2, 20–22.5, and 2–4, respectively.