Carbon nanotube(CNT)/polymer nanocomposites have vast application in industry because of their light mass and high strength. In this work, a cylindrical tube which is made up of functionally graded(FG) PmP V/CNT nanocomposite, is optimally designed for the purpose of torque transmission. The main confining parameters of a rotating shaft in torque transmission process are mass of the shaft, critical speed of rotation and critical buckling torque. It is required to solve a multi-objective optimization problem(MOP) to consider these three targets simultaneously in the process of design. The three-objective optimization problem for this case is defined and solved using a hybrid method of FEM and modified non-dominated sorting genetic algorithm(NSGA-II), by coupling two softwares, MATLAB and ABAQUS. Optimization process provides a set of non-dominated optimal design vectors. Then, two methods, nearest to ideal point(NIP) and technique for ordering preferences by similarity to ideal solution(TOPSIS), are employed to choose trade-off optimum design vectors. Optimum parameters that are obtained from this work are compared with the results of previous studies for similar cylindrical tubes made from composite or a hybrid of aluminum and composite that more than 20% improvement is observed in all of the objective functions. Carbon nanotube (CNT) / polymer nanocomposites have vast application in industry because of their light mass and high strength. In this work, a cylindrical tube which is made up of functionally graded (FG) PmP V / CNT nanocomposite, is optimally designed for the The main confining parameters of a rotating shaft in torque transmission process are mass of the shaft, critical speed of rotation and critical buckling torque. It is required to solve a multi-objective optimization problem (MOP) to consider these three targets simultaneously in the process of design. The three-objective optimization problem for this case is defined and solved using a hybrid method of FEM and modified non-dominated sorting genetic algorithm (NSGA-II), by coupling two softwares, MATLAB and ABAQUS. Optimization method provides a set of non-dominated optimal design vectors. Then, two methods, nearest to ideal point (NIP) and technique for ordering preferences by similarity to ideal solution (TOPSIS), are employed to choose trade-off optimum design vectors. Optimum parameters that are obtained from this work are compared with the results of previous studies for similar cylindrical tubes made from composite or a hybrid of aluminum and composite that more than 20% improvement is observed in all of the objective functions.