Because tunnels generally have tubular shapes, the distribution of tie points between adjacent scans is usually limited to a narrow region, which makes the problem of registration error accumulation inevitable. In this paper, a global registration method is proposed based on an augmented extended Kalman filter and a central-axis constraint. The point cloud registration is regarded as a stochastic system, and the global registration is considered to be a process that recursively estimates the rigid transformation parameters between each pair of adjacent scans. Therefore, the augmented extended Kalman filter (AEKF) is used to accurately estimate the rigid transformation parameters by eliminating the error accumulation caused by the pair-wise registration. Moreover, because the scanning range of a terrestrial laser scanner can reach hundreds of meters, a single scan can cover a tunnel segment with a length of more than one hundred meters, which means that the central axis extracted from the scan can be employed to control the registration of multiple scans. Therefore, the central axis of the subway tunnel is first determined through the 2D projection of the tunnel point cloud and curve fitting using the RANSAC (RANdom SAmple Consensus) algorithm. Because the extraction of the central axis by quadratic curve fitting may suffer from noise in the tunnel points and from variations in the tunnel, we present a global extraction algorithm that is based on segment-wise quadratic curve fitting. We then derive the central-axis constraint as an additional observation model of AEKF to optimize the registration parameters between each pair of adjacent scans. The proposed approach is tested on terrestrial point clouds that were acquired in a subway tunnel. The results show that the proposed algorithm is capable of improving the accuracy of aligning multiple scans by 48%.