Abstract A stress-insensitive vector curvature sensor based on a single fiber Bragg grating (FBG) is proposed and experimentally demonstrated. The sensor is easily fabricated by encapsulating an FBG on a thin steel plate with ultraviolet glue. When the FBG deviates from the neutral plane, its effective refractive index and grating constant are changed by bending, therefore, the sensor can realize the curvature measurement. The sensitivity of the sensor in convex bending is 553.65 pm/m−1 in the range of 0.4798–1.3569 m−1. The sensor can realize vector measurement of curvature due to the opposite stress direction on the two sides of the neutral plane during bending. The concave curvature sensitivity of the sensor is −811.19 pm/m−1 in the range of 0.4798–1.3569 m−1. Due to the large stiffness of the thin steel plate, the package of the FBG makes it insensitive to small axial stress. The favorable stability of the sensor facilitates its practical application in the measurement of curvature and inclination. This sensor has the advantage of simple manufacture, low cost, and easy industrial production.