A numerical method for simulating gas-liquid-solid three-phase flows in a slurry bubble column reactor was developed based on a mixing model and an artificial neural network (ANN). Macroscopic variables required for the mathematical closure of the mixing model, such as the gas holdup, dispersion coefficient, and reaction rate, were evaluated by use of ANN, rather than empirical correlations. In contrast to the empirical correlations, ANN possesses the following advantages: (1) it is applicable to a wide range of flow conditions owing to its generalization ability, and (2) the accuracy is easily improved through a learning process using an up-to-date database. For the validation of ANN, gas holdups in an air-water bubble column were measured. Then simulations of gas-liquid-solid three-phase flows in a Fischer-Tropsch (FT) reactor were carried out using the combination of the mixing model and ANN to demonstrate its potential. The results obtained are as follows: (1) ANN accurately evaluates the gas holdups in the air-water bubble column, (2) the combination of the mixing model and ANN gives good predictions for CO conversions in FT synthesis, and (3) the accuracy of ANN is easily improved through the re-learning process. These results imply that the proposed method can be a framework for simulating multiphase flows in large industrial systems.