Abstract A global design of an erbium-doped fiber and an open-loop erbium-doped fiber amplifier (EDFA) in a steady-state operation is discussed by applying genetic algorithms. Taking a signal gain and a bandwidth as objective functions, 7 parameters of the EDFA (erbium concentration, core radius, erbium-doped radius, refractive index difference, fiber length, pumping wavelength and signal power) are optimized by solving optical propagation equations, assuming a homogenous two-level active medium and a single-mode propagation. There is evidence to show that the 1480 nm pump utilized in usual EDFAs is not an optimal choice, which should be chosen around 1460 nm . The optimal core radius ranges 0.465 – 0.548 μm on pumping power 50 – 200 mW . Under different design objects and with different pumping powers, however, there are different optimal Er-doped concentrations, reflective index differences and fiber lengths. As a single fiber EDFA, 35 dB signal gain or 35 nm bandwidth is obtained with the 7 optimal parameters, 100 mW pumping power and 0.001 mW input signal power.