This paper presents a semi-parametric model-based adaptive control method for the regulation of aortic pressure (AoP) in an <i>ex situ</i> heart perfusion (ESHP) system. The semi-parameter dynamic model of the perfusion system includes a three-element model with a capacitor and two resistors to describe the reference relationship between the aortic pressure and perfusion flow, and a data-driven model to describe the nonlinearity and the uncertainty of the perfusion system. This semi-parametric model gains high accuracy of ESHP model parameters with small size of samples in real time. We integrate the semi-parametric model in an adaptive controller which tunes the control parameters based on the personalized ESHP model to regulate the AoP to maintain the heart's physiological aerobic metabolism. Simulations and experiments (55<inline-formula><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula>5kg pigs, <inline-formula><tex-math notation="LaTeX">$\boldsymbol{n}$</tex-math></inline-formula>=6) show that the proposed semi-parametric model achieved high accuracy (0.04mmHg) ESHP model personalization in real time (0.55<inline-formula><tex-math notation="LaTeX">$\pm$</tex-math></inline-formula>0.23s) with a small overshoot less than 2mmHg.