The prevalent scene text detection approach follows four sequential steps comprising character candidate detection, false character candidate removal, text line extraction, and text line verification. However, errors occur and accumulate throughout each of these sequential steps which often lead to low detection performance. To address these issues, we propose a unified scene text detection system, namely Text Flow, by utilizing the minimum cost (min-cost) flow network model. With character candidates detected by cascade boosting, the min-cost flow network model integrates the last three sequential steps into a single process which solves the error accumulation problem at both character level and text line level effectively. The proposed technique has been tested on three public datasets, i.e, ICDAR2011 dataset, ICDAR2013 dataset and a multilingual dataset and it outperforms the state-of-the-art methods on all three datasets with much higher recall and F-score. The good performance on the multilingual dataset shows that the proposed technique can be used for the detection of texts in different languages.