SUMMARY A deep understanding of earthquake physics requires a large amount of numerical simulations on seismic wave propagation and dynamic rupture. However, the corresponding intensive computational expense of simulations at traditional CPU (central processing unit) platforms make related researches time-consuming. There are many mature graphics processing unit (GPU) programs that can dramatically accelerate the calculation of seismic wave propagation. Unfortunately, there are few discussions about GPU implementations for rupture dynamics. In this work, we extend our 3-D curved-grid finite-difference method (CG-FDM) for rupture dynamics to the GPU platform using the CUDA (compute unified device architecture) programming language. By taking advantage of the new features of the NVIDIA Volta architecture, we implement the GPU-based program for rupture dynamics that is not only efficient but also easy to maintain. The GPU-based CG-FDM program is two orders of magnitude faster than our previous serial CPU-based program and still has a considerable advantage compared with the parallel one. The reliability and correctness of the program are carefully examined by the comparisons of the benchmarks from the ‘Southern California Earthquake Center/U.S. Geological Survey (SCEC/USGS) Dynamic Earthquake Rupture Code Verification Exercise’. The performance improvements of the GPU-based CG-FDM can save a lot of computing time, allowing researchers to perform much more numerical simulations of rupture dynamics to reveal more details of earthquake physics.