In this paper, we investigate the relationships between asymptotic average shadowing property for nonuniformly expanding maps with some notions in dynamical systems. We prove that if nonuniformly expanding (NUE) map f has asymptotic average shadowing property (AASP), then f is transitive and weakly mixing. Finally as a remark we show that if the C² diffeomorphism f is NUE and AASP then it has a unique SRB measure.