Speech bandwidth extension (SBE) assumes that high-frequency components of a speech signal, e.g., the frequency band of 4-7 kHz, can be estimated by parameters extracted from the narrowband signal (0-4 kHz). Therefore, it is very important to understand the characteristics of the highband signal as well as perceptual cues to represent the highband signal. This letter proposes a new SBE algorithm using a temporal envelope model. The temporal envelope model considers band-limited temporal envelopes as the perceptual cue of the 4-7 kHz band signal while it deemphasizes the importance of rapidly varying components. To implement the SBE with no additional bits, the proposed method adopts a Gaussian mixture model (GMM) to estimate the temporal envelope of the highband signal from that of the narrowband one. Simulation results confirm that the proposed SBE algorithm shows better perceptual quality than a conventional source-filter model-based approach.