We report on a high-performance curvature sensor based on a long-period grating (LPG) in a dual-concentric-core fiber (DCCF). The LPG is inscribed to couple light from the fundamental mode of the central core to the ring-core modes, resulting in the generation of a series of resonant dips. Two adjacent dips shift toward each other when the LPG is bent. By monitoring the variation of the wavelength interval between these two dips, this LPG can be applied in curvature measurement with a sensitivity as high as -9.046 nm/m(-1). More importantly, such a wavelength interval is almost immune to the cross impacts of temperature and axial strain, since the sensitivities to temperature and axial strain are only 2.6 pm/°C and 0.083 pm/με, respectively.