Scene text in the environment is complicated. It can exist in arbitrary text fonts, sizes or shapes. Although scene text detection has witnessed considerable progress in recent years, the detection of text with complex shapes, especially curved text, remains challenging. Datasets with adequate samples to overcome the problem presented by curved text (or other irregularly shaped text) have been introduced only recently; however, the performance of the reported methods on these datasets is unsatisfactory. Therefore, detecting arbitrarily shaped text remains a challenging. This motivated us to propose the Mask Tightness Text Detector (Mask TTD) to improve text detection performance. Mask TTD uses a tightness prior and text frontier learning to enhance pixel-wise mask prediction. In addition, it achieves mutual promotion by integrating a branch for the polygonal boundary of each text region, which significantly improves the detection performance of arbitrarily shaped text. Experiments demonstrate that Mask TTD can achieve state-ofthe-art performance on existing curved text datasets (CTW1500, Total-text, and CUTE80) and three common benchmark datasets (RCTW-17, MSRA-TD500, and ICDAR 2015). It is worth mentioning that on CTW1500, our method can outperform previous methods, especially at higher intersection over union (IoU) thresholds (16% higher than the next-best method with an IoU threshold of 0.8), which demonstrates its potential for tight text detection. Moreover, on the largest Chinese-based dataset RCTW-17, Mask TTD outperforms other methods by a large margin in terms of both the Average Precision and F-measure, showing its powerful generalization ability.