Low-Dose Computed Tomography (LDCT) technique, which reduces the radiation harm to human bodies, is now attracting increasing interest in the medical imaging field. As the image quality is degraded by low dose radiation, LDCT exams require specialized reconstruction methods or denoising algorithms. However, most of the recent effective methods overlook the inner-structure of the original projection data (sinogram) which limits their denoising ability. The inner-structure of the sinogram represents special characteristics of the data in the sinogram domain. By maintaining this structure while denoising, the noise can be obviously restrained. Therefore, we propose an LDCT denoising network namely Sinogram Inner-Structure Transformer (SIST) to reduce the noise by utilizing the inner-structure in the sinogram domain. Specifically, we study the CT imaging mechanism and statistical characteristics of sinogram to design the sinogram inner-structure loss including the global and local inner-structure for restoring high-quality CT images. Besides, we propose a sinogram transformer module to better extract sinogram features. The transformer architecture using a self-attention mechanism can exploit interrelations between projections of different view angles, which achieves an outstanding performance in sinogram denoising. Furthermore, in order to improve the performance in the image domain, we propose the image reconstruction module to complementarily denoise both in the sinogram and image domain.