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In the last two decades the efficient traffic-flow prediction of vehicles has been significant in curbing traffic congestions at freeways and road intersections and it is among the many advantages of applying intelligent transportation systems in road intersections. However, transportation researchers have not focused on prediction of vehicular traffic flow at road intersections using hybrid algorithms such as adaptive neuro-fuzzy inference systems optimized by genetic algorithms. In this research, we propose two models, namely the adaptive neuro-fuzzy inference system (ANFIS) and the adaptive neuro-fuzzy inference system optimized by genetic algorithm (ANFIS-GA), to model and predict vehicles at signalized road intersections using the South African public road transportation system. The traffic data used for this research were obtained via up-to-date traffic data equipment. Eight hundred fifty traffic datasets were used for the ANFIS and ANFIS-GA modelling. The traffic data comprised traffic volume (output), speed of vehicles, and time (inputs). We used 70% of the traffic data for training and 30% for testing. The ANFIS and ANFIS-GA results showed training performance of (R2) 0.9709 and 0.8979 and testing performance of (R2) 0.9790 and 0.9980. The results show that ANFIS-GA is more appropriate for modelling and prediction of traffic flow of vehicles at signalized road intersections. This research adds further to our knowledge of the application of hybrid genetic algorithms in traffic-flow prediction of vehicles at signalized road intersections.