A robust video stabilization algorithm, which reduces shaky camera movements and rolling-shutter distortions in video sequences, is proposed in this work. We first extract feature trajectories through a video sequence, and then transform the feature positions into rolling-free smoothed positions. Then, we set a mesh grid on each frame and warp each grid cell by matching the original features to the smoothed ones. For robust warping, we formulate a cost function based on the confidence of each feature and the reliability of 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 find the optimal grid positions in the warped frame and transform each grid cell accordingly. Experimental results show that the proposed algorithm stabilizes videos and removes rolling-shutter distortions more efficiently than conventional algorithms.