A two-layer circle waveguide model based on Long-period Fiber Gratings(LPFG)was established according to the coupling theory. The transmission spectrum of a LPFG in external media with linear Refractive Index(RI) gradient distribution was obtained by using the transfer matrix method. Simulation results show that the transmission spectral characteristics of the LPFG are strongly dependent on the RI gradient distribution of external media. When the RI gradient of external media increases

the loss depth of the transmission spectrum decreases

the 3dB bandwidth increases

and there is a good linear relationship between bandwidth and RI gradient increment. When the RI gradient of external media increases from 1.1111 × 10-7 riu/mm to 1.111 1 × 10-5 riu/mm

the gradient sensitivity can reach 2.2×107 nm·mm/riu. This result allows the high sensitivity measurement of refractive index gradient to become possible

and provides a theoretical basis for the design and production of the RI gradient sensors based on LPFGs. It may be potentially suitable for application to the measurement of biochemical reactions in the small scale liquid refractive index(RI) gradient distribution.