Bandwidth　extension　is　an　effective　technique　for　enhancing　the　quality　of　audio　signals　by　reconstructing　their　high-frequency　components.　In　this　paper,　a　novel　blind　bandwidth　extension　method　is　proposed　based　on　phase　space　reconstruction.　Phase　space　reconstruction　is　introduced　to　convert　the　low-frequency　modified　discrete　cosine　transform　coefficients　of　wideband　audio　to　a　multi-dimensional　space,　and　the　high-frequency　modified　discrete　cosine　transform　coefficients　of　the　audio　signal　are　reconstructed　by　a　non-linear　prediction　model.　The　performance　of　the　proposed　method　was　evaluated　through　objective　and　subjective　tests.　It　is　found　that　the　proposed　method　achieves　a　better　performance　than　the　typical　linear　extrapolation　method,　and　its　performance　is　comparable　to　the　conventional　efficient　high-frequency　bandwidth　extension　method.