Shape optimization of internally finned circular tube has been peformed for periodically fully developed turbulent flow and heat transfer. The physical domain considered in this study is very complicated due to periodic boundary conditions both streamwise and circumferential directions. Therefore, Pareto frontier sets of a heat exchanger can be acquired by coupling the CFD and the multi-objective genetic algorithm, which is a global optimization technique. The optimal values of fin widths $(d_1,;d_2)$ and fin height (H) are numerically obtained by minimizing the pressure loss and maximizing the heat transfer rate within ranges of $d_1=0.2sim1.5;mm,;d_2=0.2sun1.5;mm,;and;H=0.2sim1.5;mm$. The optimal values of the design variables are acquired after the fifth generation and also compared to those of a local optimization algorithm for the same geometry and conditions.