The electronic image stabilization of Unmanned Air Vehicle (UAV) video can correct the shaking motions, disorienting rotations, noisy and distorted images and other unwanted effects. It will benefit the target tracking and precision strike, and also help observers to obtain useful information. Electronic video stabilization generally contains three main steps, global motion analysis, intentional motion estimation and motion compensation. This paper mainly researches the intentional motion estimation, and presents a method of fast optimal video stabilization. This method can estimate the intentional motion of UAV video fast and accurately. This method combine the accuracy in L1 optimization method and the fast speed in Kalman filtering method, solve the hysteresis problem of Kalman filtering method and the unreal-time processing problem of L1 optimization, and achieve the better effect. At last, the method proposed in this paper was carried out and validated by actual airborne videos. The results show that the proposed method can improve the accuracy of Kalman filtering method, and its efficiency is higher than L1 optimization method.