In this paper, we propose a novel method for planning grinding trajectories on curved surfaces to improve the grinding efficiency of large aluminum alloy surfaces with welds and defect areas. Our method consists of three parts. Firstly, we introduce a deficiency positioning method based on a two-dimensional image and three-dimensional point cloud, which enables us to accurately and quickly locate the three-dimensional defective areas. Secondly, we propose a 2D weld positioning method based on the defect area and obtain the spatial position of the 3D weld by combining the relationship between 2D and 3D images. Additionally, we propose an orthogonal projection method from the point cloud to the aluminum alloy surface to calculate the weld reinforcement. Thirdly, we present a space spiral grinding trajectory planning method for complex curved surfaces based on the characteristics of the weld reinforcement, spatial position, and spatial position information of the defect area. This method shortens the grinding time of the defect area and improves efficiency. Simulation and experimental results show that our grinding trajectory planning method is more efficient than other grinding methods in removing defects from the surface of aluminum alloys. Moreover, the defect area after grinding is smoother than before.