Computed Tomography (CT) at standard doses can produce clear images, but come with the risk of ionizing radiation. CT scans with reduced x-ray dose can reduce radiation, but produce more noise. Therefore, how to remove noise from low-dose CT images effectively is an important problem to be solved in academia. Existing deep learning-based methods still suffer from poor noise reduction and loss of detail information. In order to balance the noise reduction and detail information retaining, the Fourier Supervised Attention CNN (FSACNN) is proposed in this paper. To extract high-frequency noise and provide a global receptive field for the CT images, the Fourier transform supervised attention module is proposed by transforming the images from spatial domain to the frequency domain and constrains the frequency domain feature through the supervised attention. To estimate the characteristics of noise and retain more detail information, the pixel noise feature estimation module is proposed, in which the point convolution is used to extract pixel-level noise features and integrate them with convolution features. In addition, to reduce the information loss of the output feature, caused by the encoding and decoding stage, the feature flow fusion block is also designed, in which the deep layer features, shallow layer features and frequency domain features are fused by channel attention and depth separable convolution. Comparing with the existing low-dose CT image denoising algorithms, the proposed FSACNN model achieves a good balance between noise reduction ability and retaining image content information ability.