This paper analyzes three typical mechanisms of heavy forging robot grippers: pulling with a sliding block including short- and long-leveraged grippers and pushing leveraged grippers, and uses multi-objective evolutionary genetic algorithm to design the optimal forging robot grippers. The decision variables are defined according to the geometrical dimensions of the heavy grippers, and four objective functions are defined according to gripping forces and force transmission relationships between the joints, and the constraints are yielded by the physical conditions and the structure of the grippers. Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to solve the optimization problem. Normalized weighting objective functions are used to select the best optimal solution from Pareto optimal fronts. The Pareto fronts and optimal results are compared and analyzed. An optimal model of forging robot gripper is designed. The results show the effectiveness of the optimal design. Based on similarity theory, optimum dimensions from small scale forging grippers to large scale ones can be designed, and from model to prototype experiment to test the physical features is possible.