This study presents the underactuated design of a tendon-driven bioinspired robotic gripper for the stable grasping. In this study, kinematic modeling of the bioinspired underactuated robotic gripper has been proposed and optimal design variables have been found out using multi-objective evolutionary algorithms. The obtained anthropometric data of the human hand is taken as the dimension range of the input design variables in the design optimization problem. In this study, the kinematic model of the proposed gripper is obtained, and the structural multi-objective optimization problem is formulated in the static condition of the gripper. Three fitness functions have developed from the contact forces, and some geometric constraints are considered for solving the proposed multi-objective optimization problem using multi-objective grey wolf optimization algorithm. © 2020, Springer Nature Singapore Pte Ltd.