The systolic array (SA) architecture is widely used in accelerator/AI chip design due to its excellent matrix multiplication acceleration effect. However, the mismatch between the traditional sparse matrix compression format and the SA architecture results in poor SA performance in computing sparse matrices. To solve the problem, we propose a method for co-designing the sparse compression format and SA architecture. This work proposes the Vector Group Compressed Coordinate (VGCC) data stream compression format and designs a sparse SA architecture based on hardware encoding and decoding. VGCC can handle data streams of any size without increasing the index bit width. The VGCC compression size is significantly smaller than general sparse compression formats such as COO/CSR. In a sparse matrix with a sparsity of 90%, it saves 67.13% of storage space compared to the state-of-the-art ECOO data stream compression format and achieves an average acceleration of 1.54 times. We also propose a VGCC-friendly SA architecture. Our SA architecture engine reduces logic consumption by 51.6% compared to Sparse TPU while achieving a 3.23x speedup. To mitigate the issue of high no-load rates in systolic arrays, we introduce a Data Transmission Priority (DTP) data matching algorithm. With sparsity levels ranging from 50% to 90%, the algorithm’s calculation speed is enhanced by 1.124x to 1.991x. We implemented a sparse DNN accelerator on an FPGA Zynq UltraScale+MPSoC ZCU102, utilizing the VGCC compression format proposed in this study for compressing input data. When compared to the S2 Engine, the accelerator achieved a 3.37x speed improvement in matrix multiplication with 75% sparsity, significantly enhancing the speed of sparse matrix multiplication. The accelerator achieved an average throughput of 1079.33GOP/s when inferencing DNNs.