The invention provides a control device a control method for the stable running of a gas turbine, belonging to the technical field of the control of the gas turbine. The device comprises a start control module, a revolving speed control module, a revolving speed load control module, an acceleration control module, a temperature control module, a load shedding control module, a maximum value control module, a minimum value control module, a minimum value selector and a maximum value selector. According to the invention, the safety and the stability of the running process of the gas turbine can be guaranteed, the joint debug time of the gas turbine can be shortened, and the gas turbine debugging cost for the debug control system can be reduced; and a master control system is designed by the method adopting the minimum value selector, and the control system is debugged in cooperation with a simulated mathematical model, so that the rationality and the safety of the control system can be guaranteed.