Room-temperature Raman scattering was measured in ZnWO4 up to 45 GPa. We report the pressure dependence of all the Raman-active phonons of the low-pressure wolframite phase. As pressure increases new Raman peaks appear at 30.6 GPa due to the onset of a reversible structural phase transition to a distorted monoclinic b-fergusonite-type phase. The low- and high-pressure phases coexist from 30.6 GPa to 36.5 GPa. In addition to the Raman measurements we also report ab initio total-energy and lattice-dynamics calculations for the two phases. These calculations helped us to determine the crystalline structure of the high-pressure phase and to assign the observed Raman modes in both the wolframite and b-fergusonite phases. Based upon the ab initio calculations we propose the occurrence of a second phase transition at 57.6 GPa from the b-fergusonite phase to an orthorhombic Cmca phase. The pressure evolution of the lattice parameters and the atomic positions of wolframite ZnWO4 are also theoretically calculated and an equation of state reported.