In this study, an Artificial Neural Network (ANN) model to predict the moment capacity of Fiber Reinforced Plastic (FRP) strengthened Reinforced Concrete (RC) beams exposed to fire is developed. The software ABAQUS heat transfer analysis is verified by comparison with the fire resistance test results. Through this heat transfer analysis, the temperature distribution of the beam section is determined, and 400 datasets are obtained using the moment capacity calculation method combined with the section equilibrium method. The data consist of eight input parameters: the beam width, beam height, FRP area, rebar area, concrete compressive strength, insulation thickness, concrete cover depth, and fire exposure time. The output parameter is the moment capacity. The ANN model is developed through a sensitivity study using the algorithm type and the number of hidden-layer neurons as variables. The average error between the predicted data of the developed ANN model and the target data obtained from the moment capacity calculation method was 0.35 kN·m, and the average relative error was 0.2512%, showing high accuracy. Therefore, the ANN model developed here can determine the moment capacity without complex calculations. The effects of the input parameters on the moment capacity of the FRP-strengthened RC beams exposed to fire are investigated using the ANN model.