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Ship detection of synthetic aperture radar (SAR) images has received much attention in the field of military and people's livelihood. The radar pulse signals reflected by buildings and sea clutter would reduce the salience of ships in images, making ship features blurrier. This leads to interference and erroneous judgments in SAR ship detection. To solve this problem, a novel SAR ship detection method based on salience region extraction (SRE) and multi-branch attention (MBA) is proposed in this paper. The designed SRE module extracts all regions where ships may exist according to the maximum inter-class variance, and filters out irrelevant background information. Then, the proposed MBA module is used to enhance the expressive ability of ship features, so as to improve the salience of the ship features. Extensive comparison experiments have been conducted to prove the effectiveness of SRE and MBA modules. The average precision (AP0.5) is increased by 3.20% and 2.13% through SRE module and MBA module, respectively. The proposed method could achieve 0.8966 and 0.9697 in AP0.5for inshore and offshore scenes, which gives the best results.