The heat and flow characteristics in a single-phase parallel-flow heat exchanger was examined numerically to obtain its optimal shape. A response surface method was introduced to approximately predict its performance with respect to the design parameters over the design domain. The inflow/outflow angle of the working fluid, the location of inlet/outlet, the protruding height of flat tube and the height of header were chosen as a design parameter The evaluation of the relative importance of the design parameters was performed based on a sensitivity analysis. An efficiency index was used as an evaluation characteristics value to simultaneously consider both the heat transfer and the pressure drop. The efficiency index of the optimum model, compared to that of the base model, was increased by 9.3%.