In　this　paper,　we　propose　a　wideband　(WB)　to　super-wideband　audio　bandwidth　extension　(BWE)　method　based　on　temporal　smoothing　cepstral　coefficients　(TSCC).　A　temporal　relationship　of　audio　signals　is　included　into　feature　extraction　in　the　bandwidth　extension　frontend　to　make　the　temporal　evolution　of　the　extended　spectra　smoother.　In　the　bandwidth　extension　scheme,　a　Gammatone　auditory　filter　bank　is　used　to　decompose　the　audio　signal,　and　the　energy　of　each　frequency　band　is　long-term　smoothed　using　minima　controlled　recursive　averaging　(MCRA)　in　order　to　suppress　transient　components.　The　resulting　＇steady-state＇　spectrum　is　processed　by　frequency　weighting,　and　the　temporal　smoothing　cepstral　coefficients　are　obtained　by　means　of　the　power-law　loudness　function　and　cepstral　normalization.　The　extracted　temporal　smoothing　cepstral　coefficients　are　fed　into　a　Gaussian　mixture　model　(GMM)-based　Bayesian　estimator　to　estimate　the　high-frequency　(HF)　spectral　envelope,　while　the　fine　structure　is　restored　by　spectral　translation.　Evaluation　results　show　that　the　temporal　smoothing　cepstral　coefficients　exploit　the　temporal　relationship　of　audio　signals　and　provide　higher　mutual　information　between　the　low-　and　high-frequency　parameters,　without　increasing　the　dimension　of　input　vectors　in　the　frontend　of　bandwidth　extension　systems.　In　addition,　the　proposed　bandwidth　extension　method　is　applied　into　the　G.729.1　wideband　codec　and　outperforms　the　Mel　frequency　cepstral　coefficient　(MFCC)-based　method　in　terms　of　log　spectral　distortion　(LSD),　cosh　measure,　and　differential　log　spectral　distortion.　Further,　the　proposed　method　improves　the　smoothness　of　the　reconstructed　spectrum　over　time　and　also　gains　a　good　performance　in　the　subjective　listening　tests.