In recent years, the advance of convolutional neural networks (CNNs) helped image super-resolution (SR) research to achieve remarkable improvement. However, the majority of the SR methods are non-blind, assuming the image degradation is defined (e.g., bicubic). So, these methods struggle in case of unknown degradation. Recently, a blind SR task was developed to deal with this problem using degradation estimation. Although many models have been developed for blind SR, blind SR is still a challenging problem and needs to be improved further. Therefore, this paper proposes a Fourier-based Degradation-aware Transformer-style Network (FDATSRN) for a blind image SR. The idea of the FDATSRN is based on exploring the spatial context of the input image in the Fourier space and a large receptive field for restoring the SR image. This is achieved by designing a Fourier-based degradation-aware Transformer block (FDATB) to be the backbone of the FDATSRN model. The FDATB is designed to be a lightweight version of the SR-transformer block based on using the degradation-aware convolution, convolutional modulation, and Fourier unit. Extensive experiments are performed to show the efficiency of the proposed FDATSRN in handling a large receptive field.