During intravascular interventional surgery, the 3D surgical navigation system can provide doctors with 3D spatial information of the vascular lumen, reducing the impact of missing dimension caused by digital subtraction angiography (DSA) guidance and further improving the success rate of surgeries. Nevertheless, this task often comes with the challenge of complex registration problems due to vessel deformation caused by respiratory motion and high requirements for the surgical environment because of the dependence on external electromagnetic sensors. This article proposes a novel 3D spatial predictive positioning navigation (SPPN) technique to predict the real-time tip position of surgical instruments. In the first stage, we propose a trajectory prediction algorithm integrated with instrumental morphological constraints to generate the initial trajectory. Then, a novel hybrid physical model is designed to estimate the trajectory's energy and mechanics. In the second stage, a point cloud clustering algorithm applies multi-information fusion to generate the maximum probability endpoint cloud. Then, an energy-weighted probability density function is introduced using statistical analysis to achieve the prediction of the 3D spatial location of instrument endpoints. Extensive experiments are conducted on 3D-printed human artery and vein models based on a high-precision electromagnetic tracking system. Experimental results demonstrate the outstanding performance of our method, reaching 98.2% of the achievement ratio and less than 3 mm of the average positioning accuracy. This work is the first 3D surgical navigation algorithm that entirely relies on vascular interventional robot sensors, effectively improving the accuracy of interventional surgery and making it more accessible for primary surgeons.