<p>Based on the focusing principle of the Luneburg lens in optics, a water depth expression for Luneburg lens topography was derived using the linear ray method. This topography functions as a “perfect” focusing terrain, directing all wave rays to converge at a specific point. An analytical solution for long-wave propagation over Luneburg lens topography was developed and validated using Longuet-Higgins’s analytical solution for a submerged cylinder. Through this analytical solution, the long-wave focusing mechanism over the Luneburg lens topography was systematically examined under various water depths, incident wave periods, and terrain bottom radii. The analysis revealed that the wave-focusing effect intensifies with decreasing incident wave period and water depth, and increasing terrain bottom radius. The relative scale of terrain (<i>kr</i>₀) emerges as a crucial parameter affecting wave focusing. As <i>k</i>₀<i>r</i>₀ increases, the wave-focusing effect initially intensifies before reaching stability. Furthermore, quantitative relationships were established between the maximum wave surface and its location generated by long-wave focusing over Luneburg lens topography and the relative terrain scale. Formulas for calculating the focusing wave height and focusing location were developed under linear long-wave conditions.</p>