The Pacific Decadal Oscillation (PDO) is the most prominent decadal variability in the North Pacific, which exerts profound influence on both regional and global climate. Understanding North Pacific decadal variability is vital for improving large-scale and regional climate prediction, and for discerning its worldwide influence. The decadal variability of PDO has shifted to a higher frequency in a warmer climate, but it remains unclear how the predictability of PDO will change under the greenhouse warming. Here, the response of sea surface temperature decadal-scale predictability to global warming in the North Pacific is quantified based on the Coupled Model Intercomparison Project Phase 5 multimodel outputs. We found that the upper time limit of the predictable components corresponding to the PDO decreases significantly as the greenhouse gas concentration increases. The suppressed predictability is largely attributable to an enhanced ocean stratification, facilitating accelerated propagation of baroclinic Rossby waves. Furthermore, the amplitude of predictable spatial signals weakens under greenhouse warming, which may be due to reduced wind stress curl variance. Our results indicate that greenhouse warming may impose constraint on the decadal-scale predictability of the PDO, and hence the ability to predict the associated climatic influence.