This paper explores an external gear pump's prediction of the remaining useful life (RUL). Moreover, based on Bayesian regularized radial basis function neural network (Trainbr-RBFNN) it proposes a RUL prediction method. The variational mode decomposition (VMD) algorithm has been used to denoise the vibration data of accelerated degradation test, followed by which, using the Hilbert modulation the reconstructed signal has been demodulated. After which, compared with the ensemble empirical mode decomposition (EEMD) algorithm and the modified ensemble empirical mode decomposition (MEEMD) algorithm. Subsequently, factor analysis (FA) has been selected to realize the fusion of various characteristic parameters, after which, the external gear pump's degradation evaluation index established and analyzed. Finally, the degradation evaluation index has been used to train the Trainbr-RBFNN model, and achieve gear pump degradation evaluation model for RUL prediction. Experiment results evidence that the RUL of the external gear pump can be accurately evaluated with the method used. INDEX TERMS External gear pump, Trainbr-RBFNN, remaining useful life, parameter fusion.