In in vivo optical projection tomography (OPT), object motion will significantly reduce the quality and resolution of the reconstructed image. Based on the well-known Helgason-Ludwig consistency condition (HLCC), we propose a novel method for motion correction in OPT under parallel beam illumination. The method estimates object motion from projection data directly and does not require any other additional information, which results in a straightforward implementation. We decompose object movement into translation and rotation, and discuss how to correct for both translation and general motion simultaneously. Since finding the center of rotation accurately is critical in OPT, we also point out that the system's geometrical offset can be considered as object translation and therefore also calibrated through the translation estimation method. In order to verify the algorithm effectiveness, both simulated and in vivo OPT experiments are performed. Our results demonstrate that the proposed approach is capable of decreasing movement artifacts significantly thus providing high quality reconstructed images in the presence of object motion.