Circular fringe projection profilometry（CFPP）, as a single-shot measurement method, can calculate the absolute phase from single wrapped phase distribution. However, in the existing CFPP based on Fourier transform, the fringe pattern needs to be transformed into the polar coordinate system to acquire the phase, and then the phase value needs to be transformed back into the Cartesian coordinate system. The coordinate transformation and the used interpolation operation increase the computing load and introduce some unexpected errors. To directly extract the phase information from the circular fringe, this paper investigates circular fringe projection profilometry based on windowed Fourier transform. One of the advantages is that it can avoid the influence on the reconstruction from phase errors around the center and reduce the difficulty of phase unwrapping by locating the circular center at edge region of the field of view. Furthermore, the proposed method can obtain the absolute phase from single wrapped phase by calculating the fringe order difference between the position of the circle center and the selected unwrapping starting point. In addition, in order to improve the accuracy of calculating pixel displacement amount, which relates to the height of the measured object, the inverse fringe projection technique is introduced into our method to correct the period of the reference fringes to be a constant. Both simulations and experimental results demonstrate that the circular fringe projection based on windowed Fourier transform can achieve measurements of off-plane objects, with a root mean square error less than 0.05 mm for planar and object measurements. The research work fundamentally ensures the measurement accuracy of circular fringe projection profilometry, offering advantages and reference value for fast and high-precision 3D measurements of objects in out-of-plane motion.