Separable　nonlinear　models　(SNLMs)　adopt　a　linear　combination　of　nonlinear　functions,　which　is　often　used　in　the　field　of　system　identification,　machine　learning　and　signal　processing.　In　this　paper,　we　studied　the　performance　of　gradient-based　algorithms　in　identifying　separable　nonlinear　models.　We　put　forward　a　gradient　descent-based　variable　projection　(GD-VP)　algorithm　which　taking　advantage　of　the　particular　structure　of　SNLM.　In　each　iteration,　the　algorithm　eliminates　the　linear　parameters　of　the　model,　then　updates　the　nonlinear　parameters　through　the　gradient　descent　(GD)　algorithm.　To　improve　the　convergence　rate　of　GD　algorithm,　an　accelerated　GD-VP　algorithm　is　derived　by　employing　the　Aitken　acceleration　technology.　Numerical　experiments　shows　the　efficiency　of　the　proposed　algorithm.　©　2021　IEEE.