In this study, we developed novel hybrid models namely Adaptive Neuro Fuzzy Inference System (ANFIS) optimized by Shuffled Complex Evolution (SCE) on the one hand and ANFIS with Artificial Bee Colony (ABC) on the other hand. These were used to predict compressive strength (Cs) of concrete relating to thirteen concrete-strength affecting parameters which are easy to determine in the laboratory. Field and laboratory tests data of 108 structural elements of 18 concrete bridges of the Ha Long-Van Don Expressway, Vietnam were considered. The dataset was randomly divided into a 70:30 ratio, for training (70%) and testing (30%) of the hybrid models. Performance of the developed fuzzy metaheuristic models was evaluated using standard statistical metrics: Correlation Coefficient (R), Root Mean Square Error (RMSE) and Mean Absolute Error (MAE). The results showed that both of the novel models depict close agreement between experimental and predicted results. However, the ANFIS-ABC model reflected better convergence of the results and better performance compared to that of ANFIS-SCE in the prediction of the concrete Cs. Thus, the ANFIS-ABC model can be used for the quick and accurate estimation of compressive strength of concrete based on easily determined parameters for the design of civil engineering structures including bridges.