In this study, we investigate the long-time behavior of the global solution of the anisotropic quasi-geostrophic equation, denoted by θ , where θ belongs to the space C b (R + , H s (R 2)) . Our results demonstrate that the solution decays to zero as time approaches infinity in the L p (R 2) norm, with p ≥ 2 . Additionally, we establish that the limit of ‖ θ (t) ‖ H s approaches zero as t tends to infinity.