The computed tomography setup for the opposite parallel linear scanning (OPLCT) of X-ray source and detectors is simple in structure and feasible to achieve portability or mobility. The order subset-simultaneous algebraic reconstruction algorithm has been used in the preliminary studies, but its image reconstruction time is too long to realize fast imaging. To address this problem, we proposed a filtered back-projection algorithm for OPLCT (OPLFBP) based on the Fourier’s theorem. A single translation (1T) model was constructed for image reconstruction, while this model results in limited angle problem and cannot completely reconstruct the object image using the OPLFBP algorithm. Further, a multiple translation (MT) model was proposed, and meanwhile, models for two orthogonal translations (2T) and three symmetrical translations (3T) were constructed respectively. The simulation results for the 1T, 2T and 3T modes show that the OPLFBP algorithm is effective, and the 2T and 3T scanning modes and the traditional circular scanning mode are comparable in terms of reconstrution time and image quality.