Synchrotron radiation-based full-field nano-computed tomography (CT) is capable of non-destructive detection of the internal 3D structure of samples with nanoscale spatial resolution, and has a wide range of applications. Conventional nano-CT requires the acquisition of numerous projection images to ensure the accuracy and high resolution of 3D reconstruction, which is not only time-consuming but also may cause radiation damage to the sample. In this study, a novel denoising network model, SwinCBD (Swin Transformer-based convolutional blind denoising), is proposed to address the challenges of nano-CT technology. The SwinCBD model is based on Swin Transformer and convolutional neural network to establish structural relation mapping between noisy images and clean images through deep learning to achieve high-quality reconstruction of low-dose nano-CT with low exposure and fewer projections. The experimental results show that the low-dose nano-CT image denoising based on the SwinCBD model improves the signal-to-noise ratio of the low-dose CT slice images (by 49.26%), and drastically reduces the nano-CT projections acquisition time under the premise of ensuring the image quality. The model will be important for improving the nano-CT temporal resolution and reducing the radiation damage of samples.