Numerical simulating the change of M2Q of a TEMoo Gaussian beam after homogeneously saturating amplification versus parameters of the input beam and the amplifier was performed. Calculation shows that, laser amplification always deteriorates the input beam quality, especially when the ratio of the amplifier bore diameter a to the spot size ω of the Gaussian beam ranges about 1～ 4. To get an amplified laser beam with better beam quality, low input intensity, low total gain and large saturation intensity of theamplifier is prefered.