Electricity transmission systems are essential to a community's functionalities but are susceptible to the aggressive environmental or operational factors such as the natural hazards and the environment-induced component deterioration during their service life. The service reliability of a power grid system shall be assessed under a probability-based framework taking into account the spatial uncertainty and correlation arising from both the component performance (i.e., plants, substations, and transmission lines) and the load effects. This paper estimates the resilience of a power grid system in the presence of the impacts of component deterioration and correlation, with an emphasis on the earthquake excitation hazards. The spatial variability of the component capacity and that associated with the earthquake ground motion are modeled by the Gaussian copula function. A posthazard performance indicator (PPI) is used to represent the seismic vulnerability of a grid system subjected to earthquake actions. With this, the statistics (mean value and variance) of the PPI conditional on the occurrence of an earthquake is estimated by a simulation-based method, and the resilience of the grid system (measured by a resilience index based on the recovery process of PPI) is assessed in a closed-form. The applicability of the proposed method is demonstrated through the seismic resilience assessment of an illustrative grid system.