The iterative closest point (ICP) algorithm is a classical and widely used point cloud registration algorithm. However, this algorithm has high requirements for the initial position and is computationally slow. On the other hand, improved methods based on feature extraction suffer from low registration accuracy due to insufficient or unrepresentative feature point quantities. To address this, an improved ICP registration algorithm based on dual-constraint feature extraction is proposed. Firstly, feature points are extracted using the angle between normal vectors and the intrinsic shape signature (ISS), utilizing the complementary nature of these two constraints to obtain more representative feature points. These feature points are then described using the three-dimensional shape context (3DSC) algorithm to obtain an initial point set. Next, the sample consensus initial alignment (SAC-IA) algorithm is integrated with the ICP algorithm to provide an optimized initial pose for ICP. Finally, through separate studies using multiple sets of simulated data and real-world measurements from LiDAR, the experimental results demonstrate that compared to the traditional ICP algorithm, the registration accuracy of different objects has been improved by more than 85% and the computation time has been reduced by more than 40%. The proposed algorithm still maintains excellent registration accuracy and efficiency for large datasets with significant differences in initial positions.