To solve the problem that axial strain error affects the reconstruction accuracy of optical fiber shape sensor, a shape reconstruction algorithm based on axial strain error correction is proposed. Core position deviation is the main factor that causes axial strain error. In order to obtain the core position deviation of fiber shape sensor, a theoretical error model of three-core fiber shape sensor is proposed. In order to verify the effectiveness of the model, finite element modeling and simulation were carried out by ANSYS Workbench. The core position deviation and calibration deviation were substituted into the error theoretical model, the axial strain data of the core with the position deviation was corrected, and the axial strain data at the ideal core position was compared. It is proved that the theoretical model has a good correction effect on the axial strain data with errors. In order to calculate the core position deviation of each detection point, a method of calculating the core position deviation of FBG shape sensor based on dichotomous successive approximation is proposed according to the proposed error theory model. The simulation experiment，show that the maximum position error of the reconstructed curve was increased from 1.74mm to 0.10mm. For the self-encapsulated FBG shape sensor, the maximum position error of the reconstructed space curve was increased from 19.81mm to 7.66mm.