Continuous-time quantum walk (CTQW) is a significant quantum state evolution model driven by a Hamiltonian, with notable theoretical and practical importance. However, the limitations of current quantum hardware hinder large-scale CTQW research, making classical computer simulation the preferred alternative. The matrix exponential is a computationally intensive core component of CTQW simulation, ideally suited for GPU acceleration. To address this, we developed FastCTQW, a GPU-accelerated Python simulator for ultra-large scale CTQW algorithms, based on our custom-developed matrix exponential calculation module. Experimental results demonstrate that FastCTQW achieves speedup of up to 11.85 \(\times \) , 1.59 \(\times \) , and 1.37 \(\times \) over SciPy, CuPy, and JAX respectively, notably outperforming the recent GPU-accelerated CTQW simulator QWAK by up to 4.76 \(\times \) —all with half the memory overhead of its counterparts.