We consider focusing of the surface water waves by a Luneburg lens consisting of submerged pillars of the same height. We develop the shallow water formalism for Navier-Stokes equations and solve them numerically in General PDE Module of Comsol. The complex bathymetry is obtained by matching the refractive index of the structure with the theoretical Luneburg profile. We show that the focusing performance of the lens made of submerged pillars is close to that of the "ideal" lens with continuous distribution of height.