Accurate three-dimensional shape measurement of vascular intervention surgical catheters is the key to improving surgical quality. The existing two-dimensional imaging, electromagnetic, and other methods have problems such as large measurement errors in the three-dimensional shape of catheters, which seriously restrict the safety and efficiency of surgery. This article proposes a shape reconstruction method for interventional catheters that integrates biplane perspective images and fiber Bragg grating sensing to meet the precise navigation requirements of vascular interventional surgical catheters, achieving accurate reconstruction of the three-dimensional shape of interventional surgical catheters. Firstly, based on the theory of fiber optic grating sensing, the curvature and directional angle of the grating nodes are solved. Meanwhile, to reduce the error accumulation caused by fiber optic torsion, the polar geometric stereo vision matching method is used to fuse the biplane perspective image to inverse solve the information of the conduit nodes, and the geometric parameters of the conduit curvature and directional angle reconstructed by the fiber optic grating are corrected. Finally, by combining the Frenet framework for iterative coordinate calculation, the corrected node geometric parameters are mapped to three-dimensional space to achieve accurate reconstruction of the three-dimensional shape of the interventional catheter. To evaluate the effectiveness and feasibility of the proposed fiber optic sensing interventional catheter shape reconstruction method by fusing biplane perspective images, an experimental test of catheter shape reconstruction is conducted. The results show that the proposed method can reduce the maximum reconstruction error of interventional catheter shape from 2.52 mm to 1.46 mm, which is about 42% lower than the traditional fiber optic grating shape reconstruction method. This indicates that the proposed method has broad application prospects in the precise navigation of vascular interventional surgical robots and the precise measurement of flexible robots.