Abstract In this paper, multi-fractal characteristics of speech signals are analyzed based on MF-DFA, and it is found that the multi-fractal features are influenced greatly by frame length and noise, besides, there is a little difference between them among speech frames. Secondly, motivated by framing and using frame shift to ensure the continuity and smooth transition of speech in speech signals processing, an advanced MF-DFA (MF-DFA with forward moving overlapping windows) is proposed. The length of moving overlapping windows is determined by parameter θ . Given the value of time scale s , we have MF-DFA with the maximum moving overlapping windows and MF-DFA with half overlapping windows when θ = 1 / s and θ = 1 / 2 respectively. Moreover, when θ = 1 we exactly have MF-DFA. Numerical experiments and analysis illustrate that the multi-fractal characteristics based on AMF-DFA outperform MF-DFA and MF-DMA in stability, noise immunity and discrimination.