The target classification of synthetic aperture radar (SAR) is an important technique of SAR image processing. Recently, many deep convolutional neural network (CNN)-based methods have been proposed for SAR target classification. However, feature extraction abilities of these CNN-based methods are insufficient. On the other hand, attention-based methods (e.g., swin Transformer) have the advantage of capturing the local-global features of images. Moreover, there always exists inherently noise in SAR images influenced by the process of emitted pulses, which hinders the improvement of accuracy for SAR target classification. To solve the both problems, this study explores a swin Transformer with improved blind-spot network (STr-BS) to alleviate the bad influence caused by speckle noise in SAR image and enhance the classification result. Specifically, the denoising process in STr-BS designs an improved blind-spot network in unsupervised setting without requiring the clean SAR images as input. Then, the outputs of the improved blind-spot network are as the input of the swin Transformer for the subsequent local-global feature extraction. The proposed STr-BS is tested on two public datasets (MSTAR and OpenSARShip), and the experimental results demonstrate the effectiveness of the proposed methods in comparison to other state-of-the-art approaches.