These days the closed cycle gas turbine attracts considerable attention due to : (1) The possibility of directly coupling the closed cycle gas turbine with a high temperature gas cooled reactor ; (2) the economical use of dry coolers to reduce the thermal charge of the environment ; and (3) the reduction of pollution and energy consumption, by replacing the domestic hearth by a central heating and power station. In this paper, we selected the optimal cycle from the characteristic of thermodynamic cycle for the optimal design of closed CO$_{2}$ gas turbine cycle usuable in nuclear energy power plant. Also the effects of between the parameters and thermal efficiency were investigated by computer simulation. These results and design data will be added to basics in optimal designing closed CO$_{2}$ cycle gas turbine plant.