The dependene of amplified spontaneous emission (ASE) flux on pumping rate in a dye laser amplifier (DLA) was investigated experimentally. The experimental result is analysed theoretically, and a approximated expression for the pumping rate as a function of the dye parameter (dye concentration, active length, etc.) is obtained for enabling the DLA gain energy as hjgh as possible while keeping low ASE noise. The formulas of Stored energy and small signal gain of DLA in the pumping condition are also deduced. The theoretical calculation is in good agreement with the experimental result, and can be used for design of the ultrashort pulse dye laser amplifier.