The　radial　basis　function　network-based　state-dependent　autoregressive　(RBF-AR)　model　has　been　widely　used　in　modeling　and　prediction　of　nonlinear　time　series.　The　parameter　identification　of　RBF-AR　model　can　be　reformulated　as　a　separable　nonlinear　least　squares　problem.　The　variable　projection　(VP)　algorithm　has　been　proven　to　be　valuable　in　solving　such　problems.　However,　for　ill-posed　problems,　the　classical　VP　algorithm　usually　yields　unstable　models.　In　this　paper,　we　consider　a　novel　regularized　separable　algorithm　that　takes　advantage　of　the　VP　method　and　the　expectation-maximization　(EM)　method.　The　proposed　algorithm　utilizes　the　VP　algorithm　to　optimize　the　nonlinear　parameters　and　automatically　picks　out　the　regularization　parameters　during　the　search　process.　Numerical　results　on　real-world　data　and　synthetic　time　series　confirm　the　effectiveness　of　the　proposed　algorithm.