With the prevalence of 3D scanners and 3D printers, manufacturing various 3D objects has become easier in recent years. When measuring the surface shape of an object using a 3D scanner, it is desirable to perform measurements at the highest possible resolution. However, there are many objects for which the resolution of commercial 3D scanners is insufficient. One solution to this problem is to apply super-resolution technology by measuring 3D data multiple times. It is crucial to align the 3D point clouds generated by multiple measurements accurately, but the conventional alignment methods are not accurate enough. This study aimed to improve the accuracy of the alignment process for 3D point clouds. The proposed method consists of the following four steps: (1) 3D point clouds are adaptively sampled. (2) A fast point feature histogram is used to extract features from the sampled point clouds. (3) The random sample consensus method is used to estimate an initial alignment. (4) The iterative closest point method is used to perform a precise alignment procedure. The feasibility of the proposed method is verified through experiments using real objects.