Ab initio calculations, based on the density functional theory, of the structural properties of MnWO4 wolframite compound are reported. We obtain the equilibrium volume from an equation of state with the anti-ferromagnetic (AF) and ferromagnetic configurations, AF being the lowest energy state, and the structural properties of the wolframite structure at zero pressure are obtained. We also study the wolframite structure up to a pressure of 31 GPa, and the pressure evolution of structural parameters is found to be in good agreement with the available experimental data.