A novel temperature-insensitive optical curvature sensor has been proposed and demonstrated. The sensor is fabricated by inscribing fiber Bragg gratings with short lengths into a piece of strongly coupled multicore fiber (SCMCF) and spliced to the conventional single-mode fiber. Due to the two supermodes being supported by the SCMCF, two resonance peaks, along with a deep notch between them, were observed in the reflection spectrum. The experimental results show that the depth of the notch changes with the curvature with a sensitivity up to 15.9dB/m-1 in a lower curvature range. Besides, thanks to the unique property of the proposed sensor, the notch depth barely changes with temperature. Based on the intensity demodulation of the notch depth, the temperature-insensitive curvature sensor is achieved with the cross sensitivity between the temperature, and the curvature is as low as 0.001m-1/∘C.