We have employed a 3D finite element code HFSS to calculate the output properties of a horn antenna operated at 6 GHz. Three models with different symmetric boundary conditions have been built in the HFSS simulations and the calculation results have been compared with those from analytical calculations. By using the symmetric boundary conditions, we can analyze higher order modes and calculate the corresponding antenna parameters such as peak directivity, peak gain, and radiation efficiency for the modes from TE11 up to TM03.