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Dynamic scene deblurring is a challenging problem in computer vision. It is difficult to accurately estimate the spatially varying blur kernel by traditional methods. Data-driven-based methods usually employ kernel-free end-to-end mapping schemes, which are apt to overlook the kernel estimation. To address this issue, we propose a blur-attention module to dynamically capture the spatially varying features of non-uniform blurred images. The module consists of a DenseBlock unit and a spatial attention unit with multi-pooling feature fusion, which can effectively extract complex spatially varying blur features. We design a multi-level residual connection structure to connect multiple blur-attention modules to form a blur-attention network. By introducing the blur-attention network into a conditional generation adversarial framework, we propose an end-to-end blind motion deblurring method, namely Blur-Attention-GAN (BAG), for a single image. Our method can adaptively select the weights of the extracted features according to the spatially varying blur features, and dynamically restore the images. Experimental results show that the deblurring capability of our method achieved outstanding objective performance in terms of PSNR, SSIM, and subjective visual quality. Furthermore, by visualizing the features extracted by the blur-attention module, comprehensive discussions are provided on its effectiveness.