Percutaneous coronary intervention (PCI) has gradually become the most common treatment of coronary artery disease (CAD) in clinical practice due to its advantages of small trauma and quick recovery. However, the availability of hospitals with cardiac catheterization facilities and trained interventionalists is extremely limited in remote and underdeveloped areas. Remote vascular robotic system can assist interventionalists to complete operations precisely, and reduce occupational health hazards occurrence. In this paper, a bionic remote vascular robot is introduced in detail from three parts: mechanism, communication architecture, and controller model. Firstly, human finger-like mechanisms in vascular robot enable the interventionalists to advance, retract and rotate the guidewires or balloons. Secondly, a 5G-based communication system is built to satisfy the end-to-end requirements of strong data transmission and packet priority setting in remote robot control. Thirdly, a generalized predictive controller (GPC) is developed to suppress the effect of time-varying network delay and parameter identification error, while adding a designed polynomial compensation module to reduce tracking error and improve system responsiveness. Then, the simulation experiment verifies the system performance in comparison with different algorithms, network delay, and packet loss rate. Finally, the improved control system conducted PCI on an experimental pig, which reduced the delivery integral absolute error (IAE) by at least 20% compared with traditional methods.