SPECT imaging system has shift-variant characteristics due to nonuniform attenuation of gamma-ray, collimator design, scattered photons, etc. In order to provide quantitatively accurate SPECT images, these shift-variant characteristics should be compensated in reconstruction. This paper presents a method to correct the shift-variant characteristics based on a continuous-discrete mapping model. In the proposed method, the projection data are modified using sensitivity functions so that filtered backprojection (FBP) method can be applied. Since the projection data are assumed to be acquired by narrow ray sum beams in the FBP method, narrow ray sum beams are approximated by a weighted sum of sensitivity functions of the measurement system, then the actual projection data are corrected by the weighting factors. Finally, FBP method is applied to the corrected projection data and a SPECT image is reconstructed. Since the proposed method requires the inversion of smaller matrices than the conventional algebraic methods, the amounts of calculation and memory space become smaller, and the stability of the calculation is greatly improved as well. The results of the numerical simulations are also demonstrated.