We have investigated the influence of different forms of the density dependence of the symmetry potential on spallation neutrons for p + Pb reactions at 1.2 GeV and 1.6 GeV by means of the improved ultra-relativistic quantum molecular dynamics (UrQMD) model. We find that the cascade component of the neutron spectra, with kinetic energies from 22 to 50 MeV and at forward angles from θ = 50° to 60°, is quite sensitive to the symmetry potential. The evaporation component is shown to be most sensitive to the stiffness of the symmetry potential at densities 1 ≤ ρ/ρ0 ≤ 2. The spallation data for the reactions under study are shown to be more consistent with improved UrQMD calculations employing symmetry potential of the form USym ≈ 25–30(ρ/ρ0)0.9 at ρ ≤ 2ρ0.