Shape information feedback during soft robot operations is critical for its precise control. Due to its flexible body characteristics， high flexibility is a pre-requisite for the mounted shape measurement sensor. Therefore， flexibility of fiber Bragg gratings sensing technology for soft robots was evaluated in this study. In this article， a flexible sensor based on double-layer orthogonal fiber Bragg grating for 3D shape measurement is proposed， and the structure， and measurement principle of the sensor are explained. The sensor prototype comprises two layers of 4×4 fiber Bragg gratings arrays. The curvature calibration experiments of the sensor were carried out in the horizontal and vertical directions， and the linear incremental relationship between the wavelength shift and the curvature was obtained. Then， the three-dimensional shape measurement was optimized， and the three-dimensional coordinate system was established by measuring the curvature of the spatial sensing point， and converting the curvature information into spatial coordinate information. Next， the three-dimensional shape of the measured object surface was reconstructed through interpolation and fitting to the discrete coordinate points in space. The flexibly-shape sensor can realize the three-dimensional shape perception of complex curved surfaces， with a curvature measurement error range of 2.8%-4.5%. The fiber Bragg grating flexible sensor proposed in this article can provide technical support for the shape measurement of soft robots.