This paper presents a proposal for the non-uniform gain compensation of an Erbium-doped fiber optic amplifier (EDFA) in a Wavelength Division Multiplexed (WDM) system using Fiber Bragg Gratings (FBG). In this proposal, the multilayer perceptron feed-forward artificial neural network with backpropagation was trained under the secant method (one-step secant) and was selected according to mean square error measurement. The proposal optimizes FBG parameters such as center frequency, rejection level and length in order to determine a filtering response based on a reduced number of FBGS that will be used to flatten the non-linear response of the amplifier gain and avoid the per-carrier treatment of a standard flattening filter. While an artificial neural network with a 7-10-6 structure demonstrated the feasibility of equalizing the gain of an EDFA using as few as three FBGS, a 25-18-12 structure improved the results when the configuration consisted of an FBG array of six resonances that provided similar results to that featured by the standard gain-flattening filter. The proposal was evaluated in an amplified WDM system of eight optical carriers located between 195-196.4 THz.