We report a combined experimental and theoretical study of melilite-type germanate, Sr2ZnGe2O7, under compression. In situ high-pressure X-ray diffraction and Raman scattering measurements up to 22 GPa were complemented with first-principles theoretical calculations of structural and lattice dynamics properties. Our experiments show that the tetragonal structure of Sr2ZnGe2O7 at ambient conditions transforms reversibly to a monoclinic phase above 12.2 Gpa with similar to 1% volume drop at the phase transition pressure. Density functional calculations indicate the transition pressure at, similar to 13 GPa, which agrees well with the experimental value. The structure of the high-pressure monoclinic phase is closely related to the ambient pressure phase and results from a displacive-type phase transition. Equations of state of both tetragonal and monoclinic phases are reported. Both of the phases show anisotropic compressibility with a larger compressibility in the direction perpendicular to the [ZnGe2O7](2-) sheets than along the sheets. Raman-active phonons of both the tetragonal and monoclinic phases and their pressure dependences were also determined. Tentative assignments of the Raman modes of the tetragonal phase were discussed in the light of lattice dynamics calculations. A possible irreversible second phase transition to a highly disordered or amorphous state is detected in Raman scattering measurements above 21 GPa.