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In industrial computed tomography (CT), the mismatch between the X-ray energy and the effective thickness makes it difficult to ensure the integrity of projection data using the traditional scanning model, because of the limitations of the object's complex structure. So, we have developed a CT imaging method that is based on a spherical trajectory. Considering an unrestrained trajectory for iterative reconstruction, an iterative algorithm can be used to realise the CT reconstruction of a spherical trajectory for complete projection data only. Also, an inclined circle trajectory is used as an example of a spherical trajectory to illustrate the accuracy and feasibility of this new scanning method. The simulation results indicate that the new method produces superior results for a larger cone-beam angle, a limited angle and tabular objects compared with traditional circle trajectory scanning.