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CRYSTALS-Dilithium is a lattice-based post-quantum digital signature scheme that is resistant to attacks by quantum computers and has been selected to be standardized in the NIST post-quantum cryptography (PQC) standardization process. However, the speed performance and design flexibility of the Dilithium still need to be evaluated. This paper presents a high-performance software/hardware co-design of CRYSTALS-Dilithium based on the NIST PQC round-3 parameters. High-speed pipelined hardware modules for NTT/INTT, point-wise multiplication/addition, and for SHAKE are included in the design to accelerate the time-consuming operations in Dilithium. All hardware modules are parameterized, thus allowing full support of run-time configuration to increase versatility. Moreover, the proposed software/hardware architecture and tight operating workflows reduce the data transmission overhead between the processor and other hardware modules. The hardware accelerator is implemented with a reconfigurable logic on FPGA and is integrated with the high-performance ARM Cortex-A9 processor in the Xilinx Zynq Architecture. We measure the performance of the software/hardware system for Dilithium in NIST security levels 2, 3, and 5. Compared to pure software implementations, we achieve 8.7-12.5 times speedup in Key generation, 6.3-7.3 times speedup in Sign, and 9.1-12.2 times speedup in Verify operations.