Up to present, there have been no studies concing the application of fluid-structure interaction (FSI) analysis to the lifetime estimation of multi-stage centrifugal compressors under dangerous unsteady aerodynamic excitations. In this paper, computational fluid dynamics (CFD) simulations of a three-stage natural gas pipeline centrifugal compressor are performed under near-choke and near-surge conditions, and the unsteady aerodynamic pressure acting on impeller blades are obtained. Then computational structural dynamics (CSD) analysis is conducted through a one-way coupling FSI model to predict altating stresses in impeller blades. Finally, the compressor lifetime is estimated using the nominal stress approach. The FSI results show that the impellers of latter stages suffer larger fluctuation stresses but smaller mean stresses than those at preceding stages under near-choke and near-surge conditions. The most dangerous position in the compressor is found to be located near the leading edge of the last-stage impeller blade. Compressor lifetime estimation shows that the investigated compressor can run up to 102.7 h under the near-choke condition and 200.2 h under the near-surge condition. This study is expected to provide a scientific guidance for the operation safety of natural gas pipeline centrifugal compressors.