As a powerful global registration method for point clouds, the 4-points congruent sets (4PCS) algorithm has been wildly used in the 3D scene reconstruction field. In this paper, we propose an adaptive 4PCS (A4PCS), which aims to provide a robustness rigid transformation for two or more overlapping laser scans. The proposed method only incorporates the distance information of the stereoscopic base set and a fast mechanism for congruent base extraction into 4PCS. To ensure the registration accuracy when dealing with restrictive situations, such as point clouds with small overlaps or scenes with symmetrical structures, a non-coplanar 4-points base set is adopted without extra time consumption. Besides, the adaptive set finetuning is introduced to the point pair searching process to accelerate the convergence of the algorithm. In addition, we replace the binary cost function of the original 4PCS with a modified estimator to strengthen the robustness of the proposed method. Experiments on thirteen pairs of point clouds for 3D indoor scenes, including ten regular size models and three scenes of one large-scale model, can demonstrate the accuracy and efficiency of the proposed method. INDEX TERMS Global registration, 4-points congruent sets (4PCS), rigid transformation, point clouds.