This paper proposes a general-purpose method for estimating the skew angles of document images. Rather than to derive a skew angle merely from text lines, the proposed method exploits various types of visual cues of image skew available in local image regions. The visual cues are extracted by Radon transform and then outliers of them are iteratively rejected through a floating cascade. A bagging (bootstrap aggregating) estimator is finally employed to combine the estimations on the local image blocks. Our experimental results show significant improvements against the state-of-the-art methods, in terms of execution speed and estimation accuracy, as well as the robustness to short and sparse text lines, multiple different skews and the presence of nontextual objects of various types and quantities.