This paper presents the first system for automated ex vivo perfusion of an isolated heart and regulating the heart's aortic pressure (AoP). An adaptive controller was developed for AoP regulation and maintained the heart's physiological aerobic metabolism. A mathematical model of the perfusion system was established based on a nonlinear equivalent circuit fluid flow model. The model combined with a virtual controller forms a reference model to generate the ideal trajectory of AoP. An adaptation algorithm tunes the control parameters based on the reference model and the isolated heart. Experiments were conducted using large animal hearts (55±5 kg porcine, n=6) to validate the adaptive controller's performance for stepwise and fast switching AoP references. The results confirmed that the the proposed controller is able to regulate the AoP of an isolated porcine heart in an accurate (mean error less than 2 mmHg) and fast (4~8 s of settling time) manner.