Long period fiber gratings (LPGs) in a two-core hollow eccentric fiber (TCHF) have been demonstrated experimentally. Two LPGs have been fabricated into the respective core of the TCHF by a high frequency CO2 laser. The coupling characteristics in the TCHF-LPG have been studied using the coupling mode theory (CMT). The resonant peak is mainly caused by the coupling between the core mode LP01 and cladding mode LP81. The experimental results agree well with the simulation results. Furthermore, the sensing properties of the TCHF-LPG have been investigated with respect to bending, temperature and axial strain. Compared with the LPG in the single mode fiber (SMF), the experimental results indicate that the sensitivity of the TCHF-LPGs to bending curvature is low and even very small at some bending directions. In addition, TCHF-LPGs are insensitive to the axial strain while sensitive to the temperature. Therefore, the proposed TCHF-LPGs can efficiently sense the changing temperature that is independent of the strain. Moreover, the TCHF-LPGs can also be applied to two-channel filters without signal crosstalk between two cores.