The computed laminography (CL) system has a unique advantage in aspects of large and plate-like objects imaging. We propose the parallel translation computed laminography (PTCL) system. Then, aiming at the image reconstruction of the system, the Feldkamp, Davis and Kress (FDK) algorithm is applied in the system. Due to the limited size of the detector, the system can only collect the projections of the region of interest of the object and the the total variation minimization based simultaneous algebraic reconstruction technique (SART+TV) algorithm is introduced into the object imaging. The simulation and experimental results demonstrate that both FDK and proposed method can achieve image reconstruction for PTCL. Compared with the FDK algorithm, the proposed method can reconstruct high-quality images from truncated and region of interest projections. Furtherly, it also demonstrates the feasibility of the system.