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Single photon emission computed tomography (SPECT) is one of the nuclear medical imaging techniques and widely used in the clinical applications. Cone-beam SPECT reconstruction can improve the photo density and spatial resolution of the reconstructed image. In this paper, based on our analytical fan-beam SPECT reconstruction formula with nonuniform attenuation and Feldkamp method, we present an analytical cone-beam SPECT reconstruction algorithm for the non-uniform attenuated Radon transform. The computer simulation experiments had demonstrated its accuracy and robustness.