This paper presents the design of a multiple-standard 1080 high definition (HD) video decoder on a mixed-grained reconfigurable computing platform integrating coarse-grained reconfigurable processing units (RPUs) and FPGAs. The proposed RPU, including 16×16 multi-functional processing elements (PEs), is used to accelerate compute-intensive tasks in the video decoding. A soft-core-based microprocessor array is implemented on the FPGA and adopted to speed-up the dynamic reconfiguration of the RPU. Furthermore, a mail-box-based communication scheme is utilized to improve the communication efficiency between RPUs and FPGAs. By exploiting dynamic reconfiguration of the RPUs and static reconfiguration of the FPGAs, the proposed platform achieves scalable performances and cost trade-offs to support a variety of video coding standards, including MPEG-2, AVS, H.264, and HEVC. The measured results show that the proposed platform can support H.264 1080 HD video streams at up to 57 frames per second (fps) and HEVC 1080 HD video streams at up to 52fps under 250MHz, at the same time, it achieves a 3.6× performance gain over an industrial coarse-grained reconfigurable processor for H.264 decoding, and a 6.43× performance boosts over a general purpose processor based implementation for HEVC decoding.