In this study, a Bayesian optimization (BO) based computational framework is developed to investigate the design of transcatheter aortic valve (TAV) leaflets and to optimize leaflet geometry such that its peak stress under the blood pressure of 120 mmHg is reduced. A generic TAV model is parametrized by mathematical equations describing its 2D shape and its 3D stent-leaflet assembly line. Material properties previously obtained for bovine pericardium (BP) and porcine pericardium (PP) via a combination of flexural and biaxial tensile testing were incorporated into the finite element (FE) model of TAV. A BO approach was employed to investigate about 1000 leaflet designs for each material under the nominal circular deployment and physiological loading conditions. The optimal parameter values of the TAV model were obtained, corresponding to leaflet shapes that can reduce the peak stress by 16.7% in BP and 18.0% in PP, compared with that from the initial generic TAV model. Furthermore, it was observed that while peak stresses tend to concentrate near the stent-leaflet attachment edge, optimized geometries benefit from more uniform stress distributions in the leaflet circumferential direction. Our analysis also showed that increasing leaflet contact area redistributes peak stresses to the belly region contributing to peak stress reduction. The results from this study may inspire new TAV designs that can have better durability.