It is a challenging task to achieve rapid and stable grasping of fruit and vegetable without damages for the agricultural robot. From the point of view of which most of fruits and vegetables are viscoelastic material, the viscoelastic characteristic of tomato was analyzed based on Burgers model in this article to provide a reference for the robotic grasping. First, the realtime viscoelastic parameters estimation model based on back-propagation neural network was established. The 3-11-4 network structure was applied, where the grasping force, displacement, and time were input to the model to estimate four viscoelastic parameters. The relative error was less than 15% at the 0.2-s estimation and correlation coefficient of fitting could reach to 0.99. Then, the expression of plastic deformation was derived by analyzing the dynamic characteristic of tomato based on Burgers model and Gripper's model during grasping. The minimum plastic deformation was taken as the condition to optimize the grasping speed and operation time. Finally, the result of simulation and experiment showed the feasibility of the method proposed in this article. This research can achieve the goal of reducing the grasping time of robots without damaging the fruit and provide a reference for robots grasping process optimization.