Applying an inversing method and a genetic algorithm, two radial distributions, i.e., a core graded-index and erbium-doped concentration, are optimized for an erbium-doped fiber amplifier (EDFA) in a two-level model under single-mode condition and weakly guided approximations. There is evidence to show that the core graded-index has obvious influence on the gain bandwidth of the EDFA, and simil...