Aluminum electrolytic capacitor (AEC) is one of the most pivotal components that affect the reliability of power electronic systems. The electrolyte evaporation and dielectric degradation are the two main reasons for the parametric degradation of AEC. Remaining useful life (RUL) prediction for AEC is beneficial for obtaining the health state in advance and making reasonable maintenance strategies before the system suffers shutdown malfunction, which can increase the reliability and safety. In this paper, a hybrid machine learning (ML) model with GRU and PSO-SVR is proposed to realize the RUL prediction of AEC. The GRU is used for the recursive multi-step prediction of AEC to model the times series of AEC, SVR optimized by PSO for hyper-parameters is applied for error compensation caused by recursive GRU. Finally, the proposed model is validated by two kinds of data sets with accelerated degradation experiments. Compared with the other methods, the results show that the proposed scheme can obtain greater prediction performance index of RUL under different prediction time points, which can support the technology of health management for power electronic system.