Traditional full-view 3D reconstruction systems are expensive and complex. To solve the above problems, a new algorithm for reconstructing an omnidirectional 3D scanning system is proposed based on a single Kinect and a rotating platform. The algorithm involves point cloud preprocessing, registration, minimizing global error between coordinate frames and color rectification. Firstly, RGB-D data are acquired by a Kinect sensor and preprocessed, and then a matching method is developed under the swivel table constraint for coarse registration. Further, the iterative closest point (ICP) algorithm is utilized for fine registration. Finally, for the loop closure caused by cumulative error and the color difference induced by different shooting angles, a global error correction and a color correction algorithm are conducted to improve the accuracy of the reconstruction results. Experimental results show that the reconstruction method can achieve full-view reconstruction of 3D objects and is superior to the KinectFusion method of Microsoft in accuracy.