Angle dispersive X-ray diffraction and Raman scattering studies have been carried out on Sr₂MgWO₆ up to ~28 and ~40 GPa, respectively. This compound is found to be structurally stable up to the highest pressure in this study. Bulk modulus of ambient phase is determined to be 128 ± 3.9 GPa which is in close agreement with the theoretical value of bulk modulus, 132 GPa, obtained using first principles calculations. Our first principles calculations also show that the initial tetragonal phase is more stable compared to the expected monoclinic structure up to at least 100 GPa.