Maritime surveillance is indispensable for civilian fields, including national maritime safeguarding, channel monitoring, and so on, in which synthetic aperture radar (SAR) ship target recognition is a crucial research field. The core problem to realizing accurate SAR ship target recognition is the large inner-class variance and inter-class overlap of SAR ship features, which limits the recognition performance. Most existing methods plainly extract multi-scale features of the network and utilize equally each feature scale in the classification stage. However, the shallow multi-scale features are not discriminative enough, and each scale feature is not equally effective for recognition. These factors lead to the limitation of recognition performance. Therefore, we proposed a SAR ship recognition method via multi-scale feature attention and adaptive-weighted classifier to enhance features in each scale, and adaptively choose the effective feature scale for accurate recognition. We first construct an in-network feature pyramid to extract multi-scale features from SAR ship images. Then, the multi-scale feature attention can extract and enhance the principal components from the multi-scale features with more inner-class compactness and inter-class separability. Finally, the adaptive weighted classifier chooses the effective feature scales in the feature pyramid to achieve the final precise recognition. Through experiments and comparisons under OpenSARship data set, the proposed method is validated to achieve state-of-the-art performance for SAR ship recognition.