Ship detection in remote sensing images plays a crucial role in various applications and has drawn increasing attention in recent years. However, existing multi-oriented ship detection methods are generally developed on a set of predefined rotated anchor boxes. These predefined boxes not only lead to inaccurate angle predictions but also introduce extra hyper-parameters and high computational cost. Moreover, the prior knowledge of ship size has not been fully exploited by existing methods, which hinders the improvement of their detection accuracy. Aiming at solving the above issues, in this paper, we propose a \emph{center-head point extraction based detector} (named CHPDet) to achieve arbitrary-oriented ship detection in remote sensing images. Our CHPDet formulates arbitrary-oriented ships as rotated boxes with head points which are used to determine the direction. The orientation-invariant model (OIM) is used to produce orientation-invariant feature maps. Keypoint estimation is performed to find the center of ships. Then, the size and head point of the ships are regressed. Finally, we use the target size as prior to finetune the results. Moreover, we introduce a new dataset for multi-class arbitrary-oriented ship detection in remote sensing images at a fixed ground sample distance (GSD) which is named FGSD2021. Experimental results on two ship detection datasets (i.e., FGSD2021 and HRSC2016) demonstrate that our CHPDet achieves state-of-the-art performance and can well distinguish between bow and stern. The code and dataset will be made publicly available.