Energy quality plays a critical role in the commercialization of thermoelectric generators (TEGs). In this study, a hyperbolic shape is introduced into the design of the thermoelectric (TE) couple, which is a core component of a TEG module. To this end, a one-dimensional thermodynamic model, solved using the particle swarm optimization (PSO) method, is developed to evaluate its exergy performance compared to that of the traditional cubic design. The results reveal that the TEG module with hyperbolic-shaped TE couples exhibits lower irreversibility, along with higher exergy efficiency and reduced levelized cost of energy (LCOE). Specifically, the hyperbolic design achieves improvements of up to 10.4% in LCOE and 12.9% in exergy efficiency relative to the traditional cubic design. Sensitivity analyses are further carried out with respect to four non-dimensional parameters: temperature ratio, resistance ratio, shape parameter, and area ratio. The findings show that the effects of temperature ratio and resistance ratio on exergy performance are non-monotonic, and optimal values exist for optimizing both the LCOE and efficiency. Moreover, increasing the absolute value of the shape parameter effectively enhances exergy efficiency while reducing the LCOE and irreversibility. Additionally, an optimal area ratio smaller than one is identified as beneficial for improving the LCOE and exergy efficiency, although irreversibility tends to increase with area ratio. Overall, the hyperbolic shape proves to be an effective design strategy for improving the exergy characteristics of TEG modules.