An accurate description of the screening potential induced by a hot, dense plasma is a fundamental problem in atomic physics and plasma physics, and it plays a pivotal role in the investigation of microscopic atomic processes and the determination of macroscopic physical properties, such as opacities and equations of state as well as nuclear fusion cross sections. Recent experimental studies show that currently available analytical models of plasma screening have difficulty in accurately describing the ionization-potential depression, which is directly determined by the screening potential. Here, we propose a consistent approach to determine the screening potential in dense plasmas under solar-interior conditions from the free-electron micro-space distribution. It is assumed that the screening potential for an ion embedded in a dense plasma is predominately determined by the free electrons in the plasma. The free-electron density is obtained by solving the ionization-equilibrium equation for an average-atom model to obtain the average degree of ionization of the plasma. The proposed model was validated by comparing the theoretically predicted ionization-potential depression of a solid-density Si plasma with recent experiments. Our approach was applied to investigate the screening potential and ionization-potential depression of Si plasmas under solar-interior conditions over a temperature range of 150-500eV and an electron-density range of 5.88x10^22^-3.25x10^24^cm^-3^. It can be easily incorporated into atomic-structure codes and used to investigate basic atomic processes, such as photoionization, electron-ion collisional excitation and ionization, and Auger decay, in a dense plasma.