Digital videos often suffer from undesirable camera jitters because of unstable camera motions. In this paper we present a novel video stabilization algorithm by mixed L1-L2 optimization, aiming at removing unwanted camera movements as well as keeping the original video information to the greatest extent. In the proposed algorithm, we compute smoothed camera paths that are composed of constant, linear and parabolic segments by L1 constraints, meanwhile using the L2 norm of the difference between smoothed and original camera paths to retain the video information. Different from other existing methods, there is only one parameter to control effects of two terms, which is both flexible and easy to meet different requirements in practice. We further design an efficient moving window scheme to support online processing or unlimited length video. Experimental results demonstrate the good performance of our proposed algorithm.