Groundwater management requires accurate methods for simulating and predicting groundwater processes. Data-based methods can be applied to serve this purpose. Support vector regression (SVR) is a novel and powerful data-based method for predicting time series. This study proposes the genetic algorithm (GA)–SVR hybrid algorithm that combines the GA for parameter calibration and the SVR method for the simulation and prediction of groundwater levels. The GA–SVR algorithm is applied to three observation wells in the Karaj plain aquifer, a strategic water source for municipal water supply in Iran. The GA–SVR's groundwater-level predictions were compared to those from genetic programming (GP). Results show that the randomized approach of GA–SVR prediction yields R2 values ranging between 0.88 and 0.995, and root mean square error (RMSE) values ranging between 0.13 and 0.258 m, which indicates better groundwater-level predictive skill of GA-SVR compared to GP, whose R2 and RMSE values range between 0.48–0.91 and 0.15–0.44 m, respectively.