The　separable　nonlinear　least-squares　(SNLLS)　problems　considered　in　this　article　frequently　appear　in　a　wide　range　of　research　fields,　such　as　machine　learning,　computer　vision,　system　identification,　and　signal　processing.　The　variable　projection　algorithm　proposed　by　Golub　and　Pereyra,　which　reduces　the　dimension　of　the　parameters　by　projecting　the　linear　parameters　out　of　the　problem,　is　quite　valuable　in　solving　SNLLS　problems.　Previous　implementations　of　the　variable　projection　algorithm　are　based　on　matrix　factorization.　In　this　article,　we　propose　an　iterative　implementation　of　the　variable　projection　algorithm.　Compared　with　previous　implementations　based　on　matrix　decomposition,　the　proposed　method　can　effectively　avoid　suffering　from　large　condition　number　of　the　matrix　or　even　matrix　decomposition　failure　when　dealing　with　ill-posed　SNLLS　problems.　Numerical　experiments　on　real-world　data　and　synthetic　data　show　the　efficiency　and　robustness　of　the　proposed　iterative　variable　projection　algorithm.　©　2013　IEEE.