The active spontaneous emission (ASE) is the important noise source for erbium-doped fiber amplifier (EDFA), affecting fiber laser based on the EDFA seriously. The theory and practice show that the ASE is closely related with pump methods, so the study on the ASE of erbium-doped fiber (EDF) under the condition of the pulse pumping has important scientific significance. What′s more, pulse pumping makes some sense to the mode-locked laser based on EDFA. The effects of pump pulse with different widths and amplitudes on the ASE are investigated by the theoretical and experimental methods. An approximate analytical solution of output ASE noise average is derived when pump signal is small. The results show that the output amplitude of ASE is proportional to the input width of pump pulse when the pump pulse is small. The new phenomena can be used for the all-optical measurement of a pulse width.