Through a dynamic analysis of the quad-rotor aircraft,the mechanical equilibrium equation was set up,a mathematical model of the quad-rotor aircraft was established and its state space expression was obtained.The linear quadratic design was used to control the system,and the unstable open-loop system was constructed into a stable closed-loop system,and the linear quadratic optimal control expression was provided.In order to solve the problem that it is difficult to determine the optimal weighted matrix,the weighted matrix was optimized by using the Genetic Algorithm (GA),so that the optimal weighted matrix can be found out.The optimal control system of the quad-rotor aircraft was simulated on Matlab and Simulink,and was compared with the linear quadratic control based on the experimental method.The results show that:owing to the linear quadratic optimal control based on GA,the quad-rotor aircraft has nice dynamic performance.