At present, the learning-based down-sampling method has achieved good result by using the loss of subsequent tasks to optimize the process of sampling points selection. However, for the current methods there still has two problems, on the one hand, the sampled points may not be in the original point cloud, and the sampled generated points of the sample need to be matched with the original point cloud (re-matching problem), on the other hand, the number of points obtained after matching may be insufficient for the sampling demand, which need to be supplemented by Farthest Point Sampling, nearest neighbor point, or other methods (re-supplement problem). In order to solve the above problems of re-matching and re-supplement in the learning-based sampling method, we propose a new sampling network which based on high score selection strategy. In our method, LSTM (Long Short Term Memory) is used as the feature extraction method to obtain the relational weight which relative to the subsequent tasks. The attention mechanism is used to select the high score points. The experimental results show that the performances of our network (We dubbed it as LA-Net) are better than other sampling methods and achieve the state-of-the-art in the unified benchmark. Detailed ablation studies have also been carried out, which provably affirm the advantage of each component we proposed. Finally, the methods in this paper are applied to a real backbone network to optimize its performance, and real robot grasping experiments are designed to realize automatic robot grasping of multi-target objects in real scenes.