The optical fiber curvature sensor is an important device that is widely used in the field of medical instruments. In this paper, we proposed a high sensitivity curvature sensor based on a long period fiber grating (LPFG), which is inscribed in the two-mode fiber (TMF) by CO2 laser pulses. Unlike the traditional LPFG in the single-mode fiber, TMF-LPFG couples the high-order mode LP11 in the core with the modes in the cladding. From the experiment results, the wavelength shifts to the short-wave direction as the sensor bends. This sensor offers a high curvature sensitivity of -23.67nm/m-1 in the range of 1.137-4.684m-1 and -18.95nm/m-1 in the range of 4.766-6.132m-1, respectively. Moreover, this sensor has the advantage of low transmission loss, which is less than -4dB.