Abstract: Using the characteristics of synchrotron radiation X-ray, such as high penetrability and brightness, non-destructive three-dimensional (3D) imaging of samples significantly impacts the fields including biology, materials science, and chemistry, in conjunction with the iterative reconstruction method. In flat sample systems, conventional iterative reconstruction methods like computed tomography (CT) encounter challenges in imaging size and resolution due to the high-angle missing wedge. Computed laminography (CL) has reintroduced in recent years, addressing the challenge of 3D imaging for flat samples. This paper develops a laminography Fourier iterative algorithm (LFIA) for CL, building upon the existing CT iterative reconstruction algorithm. The LFIA demonstrates superior reconstruction resolution compared to the traditional real-space iterative algorithm, and verifies through simulation and experimentation.