This　paper　proposes　a　novel　set　membership　parameter　estimation　method　for　nonlinear　systems.　According　to　the　theory　of　geometry　and　topology,　the　boundary　of　the　feasible　parameter　set　(FPS)　is　homeomorphic　to　an　n-1-sphere　(n　is　the　number　of　parameters).　From　the　viewpoint　of　manifold　learning,　the　proposed　method　constructs　a　mapping　which　can　approximate　the　homeomorphism　between　the　FPS　boundary　and　the　n-1-sphere.　Once　this　mapping　is　established,　it　can　be　used　to　map　the　n-1-sphere　into　an　approximation　of　the　FPS　boundary.　The　following　technologies　are　used　to　build　the　mapping.　First,　a　data　set　consisting　of　vectors　uniformly　sampled　from　the　FPS　boundary　is　mapped　into　a　data　set　contained　by　the　n-1-sphere.　This　is　achieved　by　Isomap　followed　by　the　data　normalization.　Then,　a　non-parametric　method　based　on　the　two　data　sets　is　used　to　build　a　mapping　which　approximates　the　homeomorphism　between　the　FPS　boundary　and　the　n-1-sphere.　The　simulation　results　show　that　the　proposed　method　exhibits　superior　accuracy　compared　with　the　support　vector　machine　method.　©　2018,　Editorial　Board　of　Journal　of　the　University　of　Electronic　Science　and　Technology　of　China.　All　right　reserved.