In order to analyze the impact of robot grasping control modes on mechanical damage of tomato, the Burgers model was used to express the deformation characteristics of tomato, and the viscoelastic parameters of tomato were obtained by the creep experiment. Three kinds of variations of speed, i.e., motion with uniform deceleration, deceleration after uniform motion and motion with variable deceleration were selected to indicate different grasping control modes. The linear function, Butterworth amplitude square function and exponential function were used to represent different grasping control modes during the robot grasping process. On this basis, the model of plastic deformation of tomato was solved, and the rules of tomato plastic deformations in different grasping control modes were analyzed when the grasping time was constant. Then, the optimal grasping strategy was selected based on the minimum plastic deformation. Experimental results indicated that the third grasping control mode was selected as the best grasping strategy, when the grasping speed was 1mm/s, the grasping time was 1s, the plastic deformation of tomato was the smallest, the early maturity and middle maturity of plastic deformations were 0.0026mm and 0.0098mm, respectively. Using the third grasping control mode to carry out the grasping control experiment, the simulation results were highly identical with measured results, the determination coefficient R2 was 0.99, which proved the rationality and feasibility of the third mode as the optimal grasping control mode. This research can offer a reference for robots grasping process optimization.