An accurate estimation of the axial compression capacity of the concrete-filled steel tubular (CFST) column is crucial for ensuring the safety of structures containing them and preventing related failures. In this article, two novel hybrid fuzzy systems (FS) were used to create a new framework for estimating the axial compression capacity of circular CCFST columns. In the hybrid models, differential evolution (DE) and firefly algorithm (FFA) techniques are employed in order to obtain the optimal membership functions of the base FS model. To train the models with the new hybrid techniques, i.e., FS-DE and FS-FFA, a substantial library of 410 experimental tests was compiled from openly available literature sources. The new model’s robustness and accuracy was assessed using a variety of statistical criteria both for model development and for model validation. The novel FS-FFA and FS-DE models were able to improve the prediction capacity of the base model by 9.68% and 6.58%, respectively. Furthermore, the proposed models exhibited considerably improved performance compared to existing design code methodologies. These models can be utilized for solving similar problems in structural engineering and concrete technology with an enhanced level of accuracy.