We propose a video stabilization algorithm, which extracts a guaranteed number of reliable feature trajectories for robust mesh grid warping. We first estimate feature trajectories through a video sequence and transform the feature positions into rolling-free smoothed positions. When the number of the estimated trajectories is insufficient, we generate virtual trajectories by augmenting incomplete trajectories using a low-rank matrix completion scheme. Next, we detect feature points on a large moving object and exclude them so as to stabilize camera movements, rather than object movements. With the selected feature points, we set a mesh grid on each frame and warp each grid cell by moving the original feature positions to the smoothed ones. For robust warping, we formulate a cost function based on the reliability weights of each feature point and each grid cell. The cost function consists of a data term, a structure-preserving term, and a regularization term. By minimizing the cost function, we determine the robust mesh grid warping and achieve the stabilization. Experimental results demonstrate that the proposed algorithm reconstructs videos more stably than the conventional algorithms.