The phase demodulation method of adaptive windowed Fourier transform (AWFT) is proposed based on Hilbert-Huang transform (HHT). HHT is analyzed and performed on fringe pattern to obtain instantaneous frequencies firstly. These instantaneous frequencies are further analyzed based on the condition of AWFT to locate local stationary areas where the fundamental spectrum will not be interfered by high-order spectrum. Within each local stationary area, the fundamental spectrum can be extracted accurately and adaptively by using AWFT with the background, which has been determined previously with the presented criterion during HHT, being eliminated to remove the zero-spectrum. This method is adaptive and unconstrained by any precondition for the measured phase. Experiments demonstrate its robustness and effectiveness for measuring the object with discontinuities or complex surface.