A 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 curvature measurement. Due to the opposite stress direction on the two sides of the neutral plane during bending, the sensor can realize vector measurement of curvature. The curvature sensitivity of the sensor in convex and concave bending is 558.42 pm/m-1 and -818.09 pm/m-1, respectively. This sensor has the advantage of simple structure, low cost, and easy industrial production. It has potential applications in engineering health monitoring and deformation measurement.