In order to realize Fourier spectrum measurement, a spectrum measurement method of windowfunction Fourier transform using incoherent illumination and single pixel detection is proposed. First, therelationship between single pixel detection spectrum reconstruction and window function Fourier transform spectrum is derived by using four step phase-shift fringe projection. Then the spectrum of three windowfunctions ,including circular function , rectangular function and rectangular transmission grating , are measured.The results show that this method can realize the measurement of the Fourier spectrum of window functions andprovide a new optical measurement method for the Fourier transform spectrum.