A method to analyze the resonant wavelength and damping decrement of the transmission spectrum of long period fiber grating (LPFG) with bending curvature was reported. Based on coupled mode theory and perturbation approximation, the general expression of transmission spectrum of LPFG according to bend curvature is deduced. Furthermore, the transmission spectrum of the bended LPFG is found to be splitting when the bending curvature is 2.56 m-1. The resonant wavelength and decrement of the split peaks change nonlinearly with the bending curvature, but the distance between split peaks changes linearly with the bending curvature. The LPFG written on the B-Ge co-doping single mode fiber proves the theory.