To improve the grasp recognition accuracy and execution stability of robots in unstructured stacked scenes, this paper proposes a 6-DOF grasp prediction algorithm that combines geometric prior modeling and a pose quality evaluation mechanism. Firstly, a point cloud recognition network named Point-Lakan is constructed. By enhancing the local geometric features of the input point cloud, a LAKAN feature extraction structure consisting of a local aggregation module and a high-dimensional nonlinear mapping module is designed to improve the structural representation ability of the stacked grasp area. Secondly, a grasp pose estimation strategy incorporating directional vector constraints is designed by minimizing the spatial difference between the initial and target poses to improve the executability and interpretability of pose generation. Finally, a grasp posture screening mechanism that combines direction constraints, collision detection, and centroid score is constructed to realize multi-factor evaluation and ranking of candidate postures, thereby enhancing the execution robustness of the algorithm in complex environments. To verify the performance of the algorithm, this paper conducts thorough evaluations using the CoppeliaSim simulation platform as well as a real-world robot system based on a self-constructed dataset of multi-category stacked object simulation point clouds for grasping tasks. The results indicate that the accuracy of grasping area recognition increases by 25.26%, while decreasing the model parameters by 4.69% and boosting the inference speed by 37.19%. In real-world grasping tasks, the success rate and task completion rate increase by up to 29.40% and 18.39%, respectively.