In this paper, a new adaptive Fourier decomposition (AFD) based time-frequency speech analysis approach is proposed. Given the fact that the fundamental frequency of speech signals often undergo fluctuation, the classical short-time Fourier transform (STFT) based spectrogram analysis suffers from the difficulty of window size selection. AFD is a newly developed signal decomposition theory. It is designed to deal with time-varying non-stationary signals. Its outstanding characteristic is to provide instantaneous frequency for each decomposed component, so the time-frequency analysis becomes easier. Experiments are conducted based on the sample sentence in TIMIT Acoustic-Phonetic Continuous Speech Corpus. The results show that the AFD based time-frequency distribution outperforms the STFT based one.