The medical treatment of cardiovascular disease can be regarded as synchronizing a chaotic diseased coronary artery system (CAS) to a healthy CAS in periodic motion. The main goal of the study is to develop a novel self-tuning integral-type finite-time-stabilized sliding mode control (IFSMC) scheme for two CASs with parameters belonging to different parameter sets to achieve their state synchronization. The defined integral-type finite-time-stabilized sliding mode (IFSM) has a special characteristic making it suitable for application to CASs. It is concluded that, on the sliding surface, one of the error states is first stabilized within a finite time. Then, the other error state becomes exponentially stable. The proposed adaptive IFSMC scheme contains four time-varying state feedback gains, which can adaptively compensate for the effects of nonlinear terms in the synchronized error dynamical system. Numerical simulations are performed to validate the effectiveness of the present scheme.