Liquid-liquid coexistence of the tetrahydrofuran (THF) + water (W) mixture was simulated in the NPT Gibbs ensemble (GE). Chemical equilibration of the two phases was provided by the transfer of molecules of each species between the two simulated boxes. To reproduce the experimental data on the THF + W liquid-liquid coexistence the electrostatic interactions between THF and W molecules has to be enhanced with respect to those describing the pure substances. The simulated coexistence curve so obtained matches approximately the localization and the shape of the immiscibility region, including the upper critical solution point (UCSP). The analysis of the pair distribution functions (PDFs) emphasizes the role played by the structural changes experienced by the W-W and THF-W interactions between the two coexisting phases. This study shows that it is possible to simulate in the Gibbs ensemble the liquid-liquid phase separation in aqueous solutions, a promising fact for the understanding of the intimate mechanisms at the origin of the demixing and for the improvement of the intermolecular potentials implemented in computer simulations.