In order to overcome the problems of poor robustness and low registration accuracy of the iterative closest point (ICP) algorithm, this paper proposes an improved ICP point cloud registration algorithm based on fast point feature histograms (FPFHs). Firstly, the point cloud feature is extracted based on the improved internal shape descriptor and the change of the normal vector angle. Secondly, an exponential function is used to improve Euclidean distance, which is used as the weight coefficient of the FPFH algorithm for describing the feature points, therefore ensuring that the initial alignment estimation obtains more accurate positions of point clouds. Then the double constraint and unit quaternion algorithm are used to complete the initial registration. Finally, in order to reduce the iteration time and reduce the influence of bad correspondence in the registration, the bidirectional k-d tree is constructed for the ICP algorithm, and the ratio of the Euclidean distance of a point pair to the maximum Euclidean distance is used to calculate the weight of each point pair, which is used as a weight coefficient of the ICP iteration error function. Experimental results show that the registration accuracy of the proposed algorithm is 2--6 orders of magnitude higher than that of the ICP algorithm, and the proposed method has stronger robustness.