The method described in this paper can be used to calculate the performance of the simple axial turbo-jet engine (one stage turbine, fixed area jet nozzle) within almost all practical revolution range including the maximum, and simpler in its procedure than any other methods already published. This can be applied, however, only for the engines in which (1) An axial compressor, of which characteristics can be represented by the two curves according to Howell's method, is used. (2) Expansion ratio of both turbine and jet nozzle are equal to or more than crytical. (3)Turbine adiabatic efficinency can be assumed constant within the range considered. These conditions simplify the power balance and mass flow balance equations, and operational matching point of every element is to be easily found by the help of graphical method. The comparisons between the published performance data of an actual engine and results of the calculation according to this paper are also presented here.