In this paper, we propose a simplified method of feature-aware for a three-dimensional point cloud. First, the k-nearest neighbor points of each point are searched by constructing an octree, and the normal vector of each point is calculated to detect and preserve the edge points. Then, the expectation maximization algorithm is utilized to cluster the point clouds and determine the points with high curvature. Finally, these point clouds are simplified by a method which utilizes the edge-aware directed Hausdorff distance, the above point clouds are merged, the duplicate points are deleted, and thus, the model is simplified. The proposed method is suitable for the models with different curvature changes, and it can display the overall contour of the model while retaining the sharp features. The experimental results show that the proposed method not only preserves the geometric features and contour appearance of the original model, but also effectively avoids the hole phenomenon in the simplification process. The geometric simplification error of the method is considerably low.