Separable　nonlinear　least-squares　(SNLLS)　problems　arise　frequently　in　many　research　fields,　such　as　system　identification　and　machine　learning.　The　variable　projection　(VP)　method　is　a　very　powerful　tool　for　solving　such　problems.　In　this　paper,　we　consider　the　regularization　of　ill-conditioned　SNLLS　problems　based　on　the　VP　method.　Selecting　an　appropriate　regularization　parameter　is　difficult　because　of　the　nonlinear　optimization　procedure.　We　propose　to　determine　the　regularization　parameter　using　the　weighted　generalized　cross-validation　method　at　every　iteration.　This　makes　the　original　objective　function　changing　during　the　optimization　procedure.　To　circumvent　this　problem,　we　use　an　inequation　to　produce　a　consistent　demand　of　decreasing　at　successive　iterations.　The　approximation　of　the　Jacobian　of　the　regularized　problem　is　also　discussed.　The　proposed　regularized　VP　algorithm　is　tested　by　the　parameter　estimation　problem　of　several　statistical　models.　Numerical　results　demonstrate　the　effectiveness　of　the　proposed　algorithm.　©　1963-2012　IEEE.