Speech bandwidth extension can be defined as the deliberate process of expanding the frequency range (bandwidth) for speech transmission. Its significant advancement in recent years has led to the technology being adopted commercially in several areas including psychoacoustic bass enhancement of small loudspeakers and the high frequency enhancement of perceptually coded audio. In this paper, a data hiding method based on dither quantization is used for speech bandwidth extension. More specifically, the out-of-band information is encoded and embedded into the narrowband speech without degrading the quality of the bandlimited signal. At the receiver, when the out-of-band information is extracted from the hidden channel, it can be used to combine with the bandlimited signal, providing a signal with a wider bandwidth. To encode the out-of-band speech more efficiently, acoustic phonetic classification is employed to generate three linear prediction (LP) codebook. The simulation results show that compared with using non-classified codebook, the propose scheme have a better bandwidth extension performance in terms of log spectral distortion (LSD).