Flying wing configuration fighter is very promising for the advanced fighter in the future. This paper studies the aerodynamic and stealth characteristics of flying wing fighter. Firstly, the effect of sharp leading edge on the subsonic, transonic lift and drag characteristics and stealth characteristics of the fighter are studied. The results show that the sharpen of leading edge of the inboard wing could greatly improve the lateral stealth characteristics while maintaining the subsonic and transonic lift characteristics. In order to furtherly improve its aerodynamic and forward stealth characteristics, the aerodynamic/stealth collaborative design optimization method based on discrete adjoint is carried out. And the results presented that there are obvious contradictions in the subsonic, transonic and supersonic lift characteristics of the flying wing fighter, and the improvement of the forward stealth characteristics will also damage the subsonic lift characteristics. Therefore, it is necessary to make a compromise between the subsonic, transonic and supersonic lift characteristics, drag characteristics and stealth characteristics in the shape design of flying wing fighter.