Coronary artery bypass grafts used to treat coronary artery disease often fail due to compliance mismatch. In this study, we have developed an experimental/computational approach to fabricate an acellular biomimetic hybrid tissue engineered vascular graft composed of alternating layers of electrospun porcine gelatin/polycaprolactone (PCL) and human tropoelastin/PCL blends with the goal of compliance-matching to rat abdominal aorta, while maintaining specific geometrical constraints. Polymeric blends at three different gelatin:PCL (G:PCL) and tropoelastin:PCL (T:PCL) ratios (80:20, 50:50 and 20:80) were mechanically characterized. The stress-strain data was used to develop predictive models, which were used as part of an optimization scheme that was implemented to determine the ratios of G:PCL and T:PCL and the thickness of the individual layers within a tissue engineered vascular graft that would compliance match a target compliance value. The hypocompliant, isocompliant, and hypercompliant grafts had target compliance values of 0.000256, 0.000568 and 0.000880 mmHg-1, respectively. Experimental validation of the optimization demonstrated that the hypercompliant and isocompliant grafts were not statistically significant from their respective target compliance values (p-value=0.37 and 0.89, respectively). The experimental compliance value of the hypocompliant graft was statistically significant than their target compliance value (p-value=0.047). We have successfully demonstrated a design optimization scheme that can be used to fabricate multilayered and biomimetic vascular grafts with targeted geometry and compliance.