In this paper, we propose a GPU-based QC-LDPC decoder for 5G New Radio(NR). Different from exist LDPC decoders based on GPUs, our decoder achieves high throughput when decoding LDPC codes with high code rates. Moreover, we implement the shortening and puncturing techniques which are exploited by 5G NR. The decoding algorithm MSA is optimized to implement efficient parallel decoding on the GPU. In order to save the on-chip and the off-chip bandwidth, we propose the two-level quantization scheme and implement data packing on the GPU. We also analyse the optimum thread assignment for different code rates based on our implementation. By using the optimum settings on the GPU, the decoding throughput achieves 1.38 Gbps in the case of (2080, 1760), r=5/6 on Nvidia RTX 2080Ti.