A filtered backprojection (FBP) algorithm is derived based on Feldkamp's FBP algorithm for a cone beam geometry that has a displaced center of rotation. In cone beam single photon emission computed tomography (CB-SPECT) the center of rotation displacement can degrade the reconstructed images. The center of rotation displacement of interest is mechanical shift, which is the displacement of the midplane of the cone beam collimator off the rotation center. Mechanical shift is characterized by two orthogonal components: the shift of the midplane of the cone beam collimator along the direction of the axis of rotation, and the distance between the midline of the cone beam collimator and the axis of rotation. This new algorithm corrects mechanical shift directly by incorporating mechanical shift into the algorithm. This new algorithm is evaluated using both Monte Carlo simulated data and experimentally acquired data. The results demonstrate that this algorithm is able to correct for blurring and the "doughnut" type artifacts caused by system mechanical shift and improve the image resolution.