The pre-neutron-emission mass distributions for reaction $^{238}$U(n, f) up to 60 MeV are systematically studied with an empirical fission potential model. The energy dependence of the peaks and valleys of the pre-neutron-emission mass distributions is described by an exponential form based on the newly measured data. The energy dependence of evaporation neutrons before scission is also considered, which plays a crucial role for the reasonable description of the mass distributions. The measured data for the pre-neutron-emission mass distributions for reaction $^{238}$U(n, f) are reasonably well reproduced up to 60 MeV. The mass distributions at unmeasured energies are also predicted with this approach.