Considering　the　uncertainty　of　hidden　neurons,　choosing　significant　hidden　nodes,　called　as　model　selection,　has　played　an　important　role　in　the　applications　of　extreme　learning　machines(ELMs).　How　to　define　and　measure　this　uncertainty　is　a　key　issue　of　model　selection　for　ELM.　From　the　information　geometry　point　of　view,　this　paper　presents　a　new　model　selection　method　of　ELM　for　regression　problems　based　on　Riemannian　metric.　First,　this　paper　proves　theoretically　that　the　uncertainty　can　be　characterized　by　a　form　of　Riemannian　metric.　As　a　result,　a　new　uncertainty　evaluation　of　ELM　is　proposed　through　averaging　the　Riemannian　metric　of　all　hidden　neurons.　Finally,　the　hidden　nodes　are　added　to　the　network　one　by　one,　and　at　each　step,　a　multi-objective　optimization　algorithm　is　used　to　select　optimal　input　weights　by　minimizing　this　uncertainty　evaluation　and　the　norm　of　output　weight　simultaneously　in　order　to　obtain　better　generalization　performance.　Experiments　on　five　UCI　regression　data　sets　and　cylindrical　shell　vibration　data　set　are　conducted,　demonstrating　that　the　proposed　method　can　generally　obtain　lower　generalization　error　than　the　original　ELM,　evolutionary　ELM,　ELM　with　model　selection,　and　multi-dimensional　support　vector　machine.　Moreover,　the　proposed　algorithm　generally　needs　less　hidden　neurons　and　computational　time　than　the　traditional　approaches,　which　is　very　favorable　in　engineering　applications.