A fast implementation of the convolution backprojection(CBP)algorithm in spotlight synthetic aperture radar(SAR)is presented based on the fast Fourier transform(FFT).Traditionally,the computation of the 'backprojection' process is expensive,since resampling in the process is implemented by using the interpolation operation.By analyzing the relative location relationship among different pixels,the algorithm realizes the 'backprojection' using a series of FFTs instead of the interpolation operation.The point target simulation validates that the new algorithm accelerates the CBP algorithm,and the computational rate increases about 85%.