Ocean data for instance segmentation is scarce and labeling is complex and time-consuming. A weakly supervised instance segmentation method using a ship dataset labelled only with bounding box annotations to achieve instance segmentation of ocean objects. We propose Object-BoxInst to improve ocean object instance segmentation performance without mask annotations. Object-BoxInst activates the object features in the box region of the class features and fuses them with the mask features to enhance the semantic information for mask prediction. Meanwhile, we build a Box Supervised Ocean Object InsSeg Dataset with 10,692 ship images and six classes. That has great significance to the application in the ocean field. The comparison experiment results show that Object-BoxInst has 40.21% AP, which is higher than BoxInst, thus effectively improving the ocean object accuracy of box-supervised segmentation.