Intergranular corrosion is the main corrosion type of Al-Cu-Mg aluminum alloys, which seriously reduce the lifetime of aircraft structural parts. In this paper, the microstructure and the intergranular corrosion behavior of 2024 alloy with varying Cu and Mg content were studied by using a scanning electron microscope (SEM), transmission electron microscope (TEM), and three-dimensional atom probe (3DAP). The results show that nano-scale θ (Al2Cu) and S (Al2CuMg) particles precipitate along grain boundaries after quenching. The nano-cluster is the main strengthening phase in the 2024 alloy after natural aging for 96 h. The intergranular corrosion susceptibility is greatly affected by the presence of θ (Al2Cu) and S (Al2CuMg) phases along grain boundaries. Specifically, Cu-rich precipitates and intermetallics are known to act as local cathodes, which facilitates the action of oxygen reduction and ultimately drives anodic dissolution of the surrounding matrix material. The intergranular corrosion resistance of the alloy decreases with the increase in Cu and Mg contents. The alloy with a lower Mg content shows better corrosion resistance than the commonly used one with a Cu to Mg mass ratio of 2.9. The relationship between the observed corrosion behavior and various contents of Cu and Mg elements is discussed, which has potential to benefit the composition design of 2xxx aluminum alloy with high corrosion resistance.