Artificial neural networks (ANNs) have recently been used to predict the hydraulic head in well locations. In the present work, the particle swarm optimization (PSO) algorithm was used to train a feed-forward multi-layer ANN for the simulation of hydraulic head change at an observation well in the region of Agia, Chania, Greece. Three variants of the PSO algorithm were considered, the classic one with inertia weight improvement, PSO with time varying acceleration coefficients (PSO-TVAC) and global best PSO (GLBest-PSO). The best performance was achieved by GLBest-PSO when implemented using field data from the region of interest, providing improved training results compared to the back-propagation training algorithm. The trained ANN was subsequently used for mid-term prediction of the hydraulic head, as well as for the study of three climate change scenarios. Data time series were created using a stochastic weather generator, and the scenarios were examined for the period 2010–2020.