Abstract: To improve the reconstruction speed of CT image reconstruction based on fan-beam filtered back-projection(FBP), this paper proposes a fast reconstruction method for the back-projection algorithm of the polar coordinates based on the features of sine and cosine function. The projection data from CT scanning of the fan-beam with equidistant detectors are firstly weighted and convolution filtered, and secondly the preprocessing projection data are back-projected on the polar coordinates reconstruction grid using the features of sine and cosine function. The experimental results showed that, compared with the traditional convolution back-projection algorithm, this method could improve the speed by more than 4 times, and the reconstruction quality was as good as that of the traditional convolution back-projection. The algorithm can also be applied to multi-slice helical 3D cone-beam reconstruction.