According to the driving potential of a fissile system, we propose a phenomenological fission potential for a description of the pre-neutron emission mass distributions of neutron-induced actinide fission. Based on the nucleus-nucleus potential with the Skyrme energy-density functional, the driving potential of the fissile system is studied considering the deformations of nuclei. The energy dependence of the potential parameters is investigated based on the experimental data for the heights of the peak and valley of the mass distributions. The pre-neutron emission mass distributions for reactions 238U(n, f), 237Np(n, f), 235U(n, f), 232Th(n, f) and 239Pu(n, f) can be reasonably well reproduced. Some predictions for these reactions at unmeasured incident energies are also presented.