Abstract: Fractal theoretics were applied to the analysis of fractal properties of Mandarin speech successfully. First, a new algorithm of the Arithmetical Progression Scales Gridding Dimension, based on the conventional Box Dimension, is presented to reduce the computation cost of fractal dimension of speech signals. Second, the distribution rules of fractal dimension of Mandarin speech have been obtained by calculating and statistically analyzing the Gridding Dimension of 21 consonants and 38 vowels of Mandarin speech. The preliminary experimnental results show that Mandarin speech has the scale-invariant property and the Gridding Dimension can indicate the complexity and irregularity degree of waveform of Mandarin speech. The novel discoveries in our studies imply that fractal theoretics have great potentials in the field of speech processing.