This study addresses the complex scenario where the parameters of the powertrain mounting system （PMS） of an elec tric vehicle exhibit both uncertainty and correlation. A robust design optimization method for the PMS， considering parametric un certainty and correlation， is investigated. Firstly， based on Nataf transform and Monte Carlo sampling， the Nataf-Monte Carlo （NMC） method is proposed for the uncertainty and correlation analysis of PMS inherent characteristics， where the probabilistic pa rameters are correlated. Then， an efficient method， the Nataf-arbitrary polynomial chaos expansion （NAPCE） method， is derived for PMS response analysis by integrating Nataf transformation with arbitrary polynomial chaos expansion. Next， based on the NAPCE method and correlation coefficient weighting method， a robust design optimization method for PMS is developed， ac counting for the uncertainty and correlation of responses. Finally， a numerical example is used to verify the effectiveness of the pro posed method， and the robust optimization of the system is carried out. The results show that， compared to the NMC method， the NAPCE method offers good computational accuracy and efficiency for analyzing uncertainty and correlation in PMS responses. The proposed optimization method can configure the PMS parameters reasonably and improve the robustness of system.