Abstract: In this paper a new bandwidth extension method of audio signal based on fractal theory was proposed. Firstly, Hurst exponent of the fine spectrum was estimated by means of rescaled range analysis, and the long-range dependence of the fine spectrum was statistically verified based on Hurst exponent of the fine spectrum from different audio signals. Then, the phase space of the fine spectrum of audio signal was reconstructed by delay-coordinate method, and the neighbor phase points were selected with angle cosine. The iteration function system whose attractor was similar with the center phase point was calculated by the neighbor phase points, according to the dependency between the center phase point and the neighbor phase points. A fractal prediction model was established to recover the fine spectrum of high-frequency components of audio signals further. Finally, by combining with the high frequency energy estimation of Gaussian mixture model, the bandwidth of audio signals was extended to super-wideband from wideband. Both the objective and subjective test results demonstrate that the proposed algorithm outperforms the conventional blind bandwidth extension algorithms.