The linearly chirped long period grating with special refractive index for EDFA gain flattening is presented. Runge-Kutta algorithm is used to numerically solve the coupled-mode equations of this type of grating. The grating structure parameters including grating length, period, linear chirp coefficient and the core refractive index profile are optimized by Nelder-Mead arithmetic. A linearly chirped long period grating with appropriate parameters is designed to flatten the gain spectrum of EDFA. The flattened gain spectrum has a bandwidth of 35 nm in C wave band and a fluctuation in ±0.5 dB.