A multicore fiber Bragg grating (FBG)-based curvature sensor interrogated by a matched-filter technique is proposed and experimentally demonstrated. The multicore FBG-based fiber curvature sensor consists of two FBGs inscribed at two arbitrary outer cores arranged symmetrically to the center core. These two FBGs have almost same reflection spectrum and center wavelength. When the multi-core fiber is bent, the overlapping area of the reflection spectra of the two FBGs changes, which affects the matched-filter output power and is related to fiber curvature. Thus we can interrogate the curvature by monitoring output power. The proposed sensor with the sensitivity of 0.78 mW·m-1 is achieved. In addition, the performances of the multicore FBG-based curvature sensor based on matched-filter interrogation under different externally applied axial strains and temperatures are also evaluated. The results show that the proposed sensor has strong ability to resist ambient fluctuations.