The　radial　basis　function　network-based　autoregressive　(RBF-AR)　model　is　a　powerful　statistical　model　which　can　be　expressed　as　a　linear　combination　of　nonlinear　functions　and　frequently　appears　in　a　wide　range　of　application　fields.　Variable　projection　algorithm　is　designed　for　solving　smooth　separable　optimization　problems　with　least　squares　form　and　has　been　used　as　an　efficient　tool　for　the　identification　of　RBF-AR　model.　However,　in　real　applications,　the　observations　are　usually　disturbed　by　non-Gaussian　noise　or　contain　outliers.　This　often　leads　to　nonlinear　regression　problems.　Since　there　are　both　linear　and　nonlinear　parameters　in　such　problems,　how　to　optimize　such　models　is　still　challenging.　In　this　paper,　we　design　a　robust　variable　projection　algorithm　for　the　identification　of　RBF-AR　model.　The　proposed　method　takes　into　account　the　coupling　of　the　linear　and　nonlinear　parameters　of　RBF-AR　model,　which　eliminates　the　linear　parameters　by　solving　a　linear　programming　and　optimizes　the　reduced　function　that　only　contains　nonlinear　parameters.　Numerical　results　on　RBF-AR　model　to　synthetic　data　and　real-world　data　confirm　the　effectiveness　of　the　proposed　algorithm.　©　2023　IEEE.