In this paper, a new method is proposed to reach high density ratios and low viscosities based on the Shan-Chen multiphase model in the lattice Boltzmann Method. In this new method the interaction force and as a result the pressure tensor is modified purposefully so that the density of the phases can be adjusted to coincide the corresponding values from the Maxwell equal area rule in thermodynamics. This leads to higher stability and therefore the mentioned purposes are achieved. This new method takes advantage of simplicity and the same implementing procedure in 2D and 3D problems with single or multi relaxation time collision operators. In order to validate the new method, first the coexistence densities of the phases at different subcritical temperatures are compared with those of the Maxwell rule, then the validity of the Laplace law for a droplet is evaluated, after that the spurious velocities around the droplet are evaluated, and finally the broken dam problem is simulated and its results are compared with an experimental data. Results show that the developed model is properly stable and is capable of simulating different multiphase flows at a wide range of density ratios and viscosities.