Due to the corrosion problem in reinforced concrete structures, the use of fiber-reinforced polymer (FRP) bars may be preferred in place of traditional reinforcing steel. FRP bars are used in concrete constructions to boost the strength of structural elements and retain their longevity. In this study, the axial load carrying capacity (ALCC) of the FRP-reinforced concrete columns has been evaluated using analytical, as well as machine learning, models. A total of fourteen popular analytical models and one proposed machine learning-based model were used to estimate the ALCC of the concrete columns. The proposed machine learning model is based on an artificial neural network (ANN) method. The performance of the ANN, as well as the analytical models, are assessed using six different performance indices. The R-value of the developed ANN model is 0.9758, followed by an NS value of 0.9513. It has been found that the mean absolute percentage error of the best-fitted analytical model is 328.71% higher than the ANN model, and the root-mean-square error value of the best-fitted analytical model is 211.97% higher than the ANN model. The evaluated data demonstrate that the proposed ANN model performs better than the other analytical models. The developed model is quick and easy-to-use to estimate the axial capacity of the FRP-reinforced concrete columns.