Curve text or arbitrary shape text is very common in real-world scenarios. In this paper, we propose a novel framework with the local segmentation network (LSN) followed by the curve connection to detect text in horizontal, oriented and curved forms. The LSN is composed of two elements, i.e., proposal generation to get the horizontal rectangle proposals with high overlap with text and text segmentation to find the arbitrary shape text region within proposals. The curve connection is then designed to connect the local mask to the detection results. We conduct experiments using the proposed framework on two real-world curve text detection datasets and demonstrate the effectiveness over previous approaches.