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Currently, reliable and accurate ship detection in optical remote sensing images is still challenging. Even the state-of-the-art convolutional neural network (CNN) based methods cannot obtain very satisfactory results. To more accurately locate the ships in diverse orientations, some recent methods conduct the detection via the rotated bounding box. However, it further increases the difficulty of detection, because an additional variable of ship orientation must be accurately predicted in the algorithm. In this paper, a novel CNN-based ship detection method is proposed, by overcoming some common deficiencies of current CNN-based methods in ship detection. Specifically, to generate rotated region proposals, current methods have to predefine multi-oriented anchors, and predict all unknown variables together in one regression process, limiting the quality of overall prediction. By contrast, we are able to predict the orientation and other variables independently, and yet more effectively, with a novel dual-branch regression network, based on the observation that the ship targets are nearly rotation-invariant in remote sensing images. Next, a shape-adaptive pooling method is proposed, to overcome the limitation of typical regular ROI-pooling in extracting the features of the ships with various aspect ratios. Furthermore, we propose to incorporate multilevel features via the spatially-variant adaptive pooling. This novel approach, called multilevel adaptive pooling, leads to a compact feature representation more qualified for the simultaneous ship classification and localization. Finally, detailed ablation study performed on the proposed approaches is provided, along with some useful insights. Experimental results demonstrate the great superiority of the proposed method in ship detection.