The coefficients of friction (COFs) is one of the most important parameters used to evaluate the braking performance of a friction brake. Many indicators that affect the safety and comfort of automobiles are associated with brake COFs. The manufacturers of friction brakes and their components are required to spend huge amounts of time and money to carry out experimental tests to ensure the COFs of a newly developed braking system meet the required standards. In order to save time and costs for the development of new friction brake applications, the GRU (Gate Recurrent Unit) algorithm optimized by the improved PSO (particle swarm optimization) global optimization method is employed in this work to predict brake COFs based on existing experimental data obtained from friction braking dynamometer tests. Compared with the LSTM (Long Short-Term Memory) method, the GRU algorithm optimized by PSO avoids the accuracy reduction problem caused by gradient descent in the training process and hence reduces the prediction error and computational cost. The combined PSO–GRU algorithm increases the coefficient of determination (R 2) of the prediction by 4.7%, reduces the MAE (mean absolute error) by 14.3%, and increases the prediction speed by 40.1% compared with the standalone GRU method. The prediction method based on machine learning proposed in this study can not only be applied to the prediction of automobile braking COFs but also for other frictional system problems, such as the prediction of braking noise and the friction of various bearing transmission components.