Generally,the energy density distribution of a TEA CO₂ laser was flat-topped. In order to find a new method for studying and analyzing the output beams of TEA CO₂ lasers,according to the FGB theory,the energy density distribution of the measured flat-top beam output by a TEA CO₂ laser was expanded in Hermit-Gauss functions. And the space distribution characteristics of the output beam were analyzed and investigated. It was proven that the energy density distribution of a TEA CO₂ laser could be expanded in Hermit-Gauss functions.