Purpose Robotic CTs can achieve customized trajectory scanning with x-ray tube and detector held by flexible robotic arms rather than fixed rails or gantry. However, the motion errors of the robotic arms cannot be neglected. Hence, the reconstruc tion method of Robotic CTs should be suitable for arbitrary trajectory and should take motion errors into full consideration. Method In this paper, we present an iterative reconstruction method for robotic CT systems. Unlike the analytical algorithms, such as FDK, this method makes no assumption about the scan trajectory. The projection and backprojection operations are modeled by 3D distance-driven algorithm using the coordinates of x-ray source and detector center fed back from the robotic arm’s positioning system directly. Both numerical simulations and practical experiments are conducted to verify the effectiveness of this method in arbitrary trajectory reconstruction and motion errors correction for robotic CT systems. Results For our non-circular and non-planar trajectory scan, this proposed method could easily handle the reconstruction and obtain a result comparable to reference. In addition, for 0.1% motion errors, using the proposed method could improve the reconstruction quality, and the RMSE could be reduced by 30%. Conclusions This iterative reconstruction method is suitable for arbitrary trajectory scans and can decrease the degradation of image quality caused by motion errors of robotic arm