Separable　nonlinear　models　are　pervasively　employed　in　diverse　disciplines,　such　as　system　identification,　signal　analysis,　electrical　engineering,　and　machine　learning.　Identifying　these　models　inherently　poses　a　non-convex　optimization　challenge.　While　gradient　descent　(GD)　is　a　commonly　adopted　method,　it　is　often　plagued　by　suboptimal　convergence　rates　and　is　highly　dependent　on　the　appropriate　choice　of　step　size.　To　mitigate　these　issues,　we　introduce　an　augmented　GD　algorithm　enhanced　with　Anderson　acceleration　(AA),　and　propose　a　Hierarchical　GD　with　Anderson　acceleration　(H-AAGD)　method　for　efficient　identification　of　separable　nonlinear　models.　This　novel　approach　transcends　the　conventional　step　size　constraints　of　GD　algorithms　and　considers　the　coupling　relationships　between　different　parameters　during　the　optimization　process,　thereby　enhancing　the　efficiency　of　the　solution-finding　process.　Unlike　the　Newton　method,　our　algorithm　obviates　the　need　for　computing　the　inverse　of　the　Hessian　matrix,　simplifying　the　computational　process.　Additionally,　we　theoretically　analyze　the　convergence　and　complexity　of　the　algorithm　and　validate　its　effectiveness　through　a　series　of　numerical　experiments.　©　The　Author(s),　under　exclusive　licence　to　Springer　Nature　B.V.　2024.