The solution of the rate equations describing an erbium-doped fiber amplifier is investigated in this paper. And the possibility of obtaining an analytical solution for some fields and erbium transverse distributions in the active fiber are determined and the solutions are calculated. The signal gain for arbitrary signal intensities (include large signal) and the main parameters that affect the signal gain are obtained. The maximum gain is as high as 29.5dB at pump wavelength of 532nm.