Aiming at the problem of robot grasping decision under different tasks of multiple objects, a learning method of the grasping strategy based on multiple constraints is proposed, in which, the characteristics of grasping objects and the attributes of grasping tasks are taken as the multiple constraints of the a robot grasping strategy. Furthermore, the method uses human grasping habit to map to robot grasp types, and the grasping rules of a robot are established by using the object bounding box(OBB). The fetching model with multiple constraints is established. Then, the radial basis function RBF network model is combined with the de-clustering algorithm SCM to realize the grasping strategy learning. The combination of the two algorithms aims to improve the robustness and accuracy of learning. Using the AUBO six-degree-of-freedom robotic arm with Reflex 1 dexterity hand, experiments are conducted to grasp objects with different shapes and multiple tasks. Experimental results show that the proposed method enables the robot to effectively learn the optimal grasping strategy for different tasks of multiple objects and has good grasping decision-making ability.