The wire-driven flexible robot with multiple bending sections is an efficient approach for the minimally invasive surgery and diagnosis. It can function properly in the complicated and restrained environment. One drawback of this technology is that the real time positional and shape information cannot be well estimated. In order to settle this limitation, we proposed a novel shape estimation method for a wire-driven flexible robot with multiple bending sections in this paper. Each bending section can be controlled independently to deform as an arc with different curvature. This method is based on the positional and directional information of limited specific joints on the robot, which can be estimated with an effective positioning method, such as electromagnetic tracking method. The number and position of these specific joints are only determined by the number of sections. Based on the positional and directional information, as well as the curve length information, the shape reconstruction algorithm can be carried out by fitting multiple quadratic B´ezier curves. Real time shape sensing platform is built to verify the proposed method. Experimental results show that the method works well and the mean position error is 1.7mm.