The response of the Pacific Decadal Oscillation(PDO) to global warming according to the Fast Ocean Atmosphere Model(FOAM) and global warming comparison experiments of 11 IPCC AR4 models is investigated. The results show that North Pacific ocean decadal variability, its dominant mode(i.e., PDO), and atmospheric decadal variability, have become weaker under global warming, but with PDO shifting to a higher frequency. The SST decadal variability reduction maximum is shown to be in the subpolar North Pacific Ocean and western North Pacific(PDO center). The atmospheric decadal variability reduction maximum is over the PDO center. It was also found that oceanic baroclinic Rossby waves play a key role in PDO dynamics, especially those in the subpolar ocean. As the frequency of ocean buoyancy increases under a warmer climate, oceanic baroclinic Rossby waves become faster, and the increase in their speed ratio in the high latitudes is much larger than in the low latitudes. The faster baroclinic Rossby waves can cause the PDO to shift to a higher frequency, and North Pacific decadal variability and PDO to become weaker. The response of the Pacific Decadal Oscillation (PDO) to global warming according to the Fast Ocean Atmosphere Model (FOAM) and global warming comparison experiments of 11 IPCC AR4 models is investigated. The results show that North Pacific ocean decadal variability, its dominant mode ( ie PDO), and atmospheric decadal variability, have become weaker under global warming, but with PDO shifting to a higher frequency. The SST decadal variability reduction maximum shown to be in the subpolar North Pacific Ocean and western North Pacific (PDO center) It was also found that oceanic baroclinic Rossby waves play a key role in PDO dynamics, especially those in the subpolar ocean. As the frequency of ocean buoyancy increases under a warmer climate, oceanic baroclinic Rossby waves become faster, and the increase in their speed ratio in the high latitudes is much larger than in the low latitudes. The faster baroclinic Rossby waves can cause the PDO to shift to a higher frequency, and North Pacific decadal variability and PDO to become weaker.