In　this　paper,　we　present　a　nonnested　augmented　subspace　algorithm　and　its　multilevel　correction　method　for　solving　elliptic　eigenvalue　problems　with　curved　interfaces.　The　augmented　subspace　algorithm　and　the　corresponding　multilevel　correction　method　are　designed　based　on　a　coarse　finite　element　space　which　is　not　the　subset　of　the　finer　finite　element　space.　The　nonnested　augmented　subspace　method　can　transform　the　eigenvalue　problem-solving　on　the　finest　mesh　to　the　solving　linear　equation　on　the　same　mesh　and　small　scale　eigenvalue　problem　on　the　low　dimensional　augmented　subspace.　The　corresponding　theoretical　analysis　and　numerical　experiments　are　provided　to　demonstrate　the　efficiency　of　the　proposed　algorithms.