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The Optimal solutions of the design variables in internally finned tubes have been obtained for three-dimensional periodically fully developed turbulent flow and heat transfer. For a trapezoidal fin profile, performances of the heat exchanger are determined by considering the heat transfer rate and pressure drop, simultaneously, that are interdependent quantities. Therefore, Pareto frontier sets of a heat exchanger can be acquired by integrating CFD and a multi-objective optimization technique. The optimal values of fin widths (d₁, d₂), fin height(h) and helix angle(r) are numerically obtained by minimizing the pressure loss and maximizing the heat transfer rate within ranges of d₁=0.5 ~1.5㎜, d₂=0.5~1.5㎜, h=0.5~1.5㎜, and r=0~20°. For this, a general CFD code and a global genetic algorithm(GA) are used. The Pareto sets of the optimal solutions can be acquired after 30 th generation.