This paper proposes Long-Range Graph Wavelet Networks (LR-GWN) to address the core challenge of long-range interaction modeling in graph machine learning. To overcome the limitations of conventional wavelet-based graph neural networks, which suffer from limited receptive fields and difficulties in long-range information propagation, LR-GWN decomposes wavelet filters into local and global components. Local aggregation uses efficient low-order polynomials, and long-range interactions are captured through flexible spectral-domain parameters, thereby integrating short-range and long-range information flow. Experimental results demonstrate that LR-GWN achieves the highest performance among wavelet-based methods on long-range benchmarks and remains competitive even on short-range datasets.