Modern audio coding technologies apply methods of bandwidth extension (BWE) to efficiently represent audio data at low bitrates. An established method is the well-known spectral band replication (SBR) that can provide the very high sound quality with imperceptible artifact. However, its bitrates and complexity are very high. Another great method is LPC-based BWE, which is part of 3GPP AMR-WB+ codec. Although its bitrates and complexity are reduced distinctly, the sound quality it provided is unsatisfactory for music. In this paper, a novel bandwidth extension method is proposed which provided the high sound quality close to eSBR, with only 0.8 kbps bitrates. The proposed method predicts the fine structure of high frequency band from low frequency band by a deep auto-encoder, and only extracts the envelope of high frequency as side information. The performance evaluation demonstrates the advantage of the proposed method compared to the state of the art. Compared with eSBR, the bitrates drop about 63 %, and the subjective listening quality is close to it. Compared with LPC-based BWE, the subjective listening quality is better than it with the same bitrates.