Gas turbines are widely used in industry, and the combustion chamber, compressor, and turbine are known as their three important components. In the design process of the combustion chamber, computational fluid dynamics simulation takes up a lot of time. In order to accelerate the design speed of the combustion chamber, this article proposes a combustion chamber design method that combines an artificial neural network (ANN) and computational fluid dynamics (CFD). CFD results are used as raw data to establish a fast prediction model using ANN and eXtreme Gradient Boosting (XGBoost). The results show that the mean squared error (MSE) of the ANN is 0.0019, and the MSE of XGBoost is 0.0021, so the ANN’s prediction performance is slightly better. This fast prediction method combines CFD and the ANN, which can greatly shorten CFD calculation time, improve the efficiency of gas turbine combustion chamber design, and provide the possibility of achieving digital twins of gas turbine combustion chambers.