The computed tomography imaging of a local region inside a sample with a size larger than the field of view is particularly important for synchrotron X-ray imaging. In this letter, an improved algorithm is proposed to reconstruct the local structure inside a sample using almost completely local data. The algorithm significantly reduces the X-ray radiation dose and improves computational efficiency. Simulation results show that the new algorithm works well and has a higher reconstruction precision than previous methods, as confirmed by experimental results carried out at the Shanghai Synchrotron Radiation Facility.