Point cloud registration is crucial in the field of computer vision. In the process of point cloud registration, coarse registration provides an initial pose for fine registration, and its accuracy severely affects the effect of point cloud registration. Existing algorithms are affected by feature extraction problems, resulting in slow registration speeds and low accuracy. To solve the above problems, this paper proposes a coarse registration algorithm based on quadratic constraint feature extraction. First, the enhanced feature points are obtained by quadratic constraint feature extraction. Then, the fast point feature histogram is used to describe these feature points. Finally, the coarse registration is accomplished by using the sampling consensus initial alignment algorithm. The point cloud data from Stanford University are used for experiments. The performance of the proposed method is evaluated using the point cloud distortion index and bidirectional hausdorff distance. Compared to existing coarse registration algorithms, the proposed algorithm improves the registration speed by 24% and the registration accuracy by 37.5%.