Interior tomography by rotary computed tomography (RCT) is an effective method to improve the detection efficiency and achieve high-resolution imaging for the region of interest (ROI) within a large-scale object. However, because only the X-rays through the ROI can be received by detector, the projection data is inevitably truncated, resulting in truncation artifacts in the reconstructed image. When the ROI is totally within the object, the solution of the problem is not unique, which is named interior problem. Fortunately, projection completion (PC) is an effective technique to solve the interior problem. In this study, we proposed a multi source translation CT based PC method (mSTCT-PC) to cope with the interior problem. Firstly, mSTCT-PC employs multi-source translation to sparsely obtain the global projection which covered the whole object. Secondly, the sparse global projection is utilized to fill up the truncated projection of ROI. The global projection and truncated projection are obtained under the same geometric parameters. Therefore, it omits the registration of projection. To verify the feasibility of this method, simulation and practical experiments were implemented. Compared with the results of ROI reconstructed by filtered back-projection (FBP), simultaneous iterative reconstruction technique-total variation (SIRT-TV) and the multi-resolution based method (mR-PC), the proposed mSTCT-PC is good at mitigating truncation artifacts, preserving details and improving the accuracy of ROI images.