The Debye screening masses of the sigma, omega and neutral rho mesons and the photon are calculated in the relativistic mean-field approximation. As the density of the nucleon increases, all the screening masses of mesons increase. A different result with Brown-Rho scaling is shown, which implies a reduction in the mass of all the mesons in the nuclear matter, except the pion. Replacing the masses of the mesons with their corresponding screening masses in the Walecka-1 model, five saturation properties of the nuclear matter are fixed reasonably, and then a density-dependent relativistic mean-field model is proposed without introducing the nonlinear self-coupling terms of mesons.