Algebraic reconstruction technique (ART) is an iterative algorithm for computed tomography (CT) image reconstruction. Due to the high computational cost, researchers turn to modern HPC systems with GPUs to accelerate the ART algorithm. However, the existing proposals suffer from inefficient designs of compressed data structure and computational kernel on GPUs. In this paper, we identify the computational patterns in the ART as the product of a sparse matrix (and its transpose) with multiple vectors (SpMV and SpMV_T). Because the implementations with well-tuned libraries, including cuSPARSE, BRC, and CSR5, underperform the expectations, we propose cuART, a complete compression and parallelization solution for the ART-based CT on GPUs. Based on the physical characteristics, i.e., the symmetries in the system matrix, we propose the symmetry-based CSR format (SCSR), which can further compress data storage by removing symmetric but redundant non-zero elements. Leveraging the sparsity patterns of X-ray projection, we transform the CSR format to multiple dense sub-matrices in SCSR. We then design a transposition-free kernel to optimize the data access for both SpMV and SpMV_T. The experimental results illustrate that our mechanism can reduce memory usage significantly and make practical datasets fit into a single GPU. Our results also illustrate the superior performance of cuART compared to the existing methods on CPU and GPU.