Ba(Mg1/2W1/2)O3 ceramic was synthesized using a conventional solid-state reaction method at 1500°C for 4 h. The face-centered cubic crystal structure of the material was confirmed by Rietveld refinement of X-ray diffraction (XRD) data, and vibrational modes were obtained by Raman and Fourier transform far-infrared (FTIR) reflection spectroscopies. First-principle calculations based on density functional theory with local density approximation were used to calculate Gamma-point modes and dielectric properties of Ba(Mg1/2W1/2)O3. The Raman spectrum with nine active modes can be fitted with Lorentzian function, and the modes were assigned as F2g(1) (126 cm−1), F2g(2) (441 cm−1), Eg(O) (538 cm−1), and A1g(O) (812 cm−1). Far-infrared spectrum with 12 infrared active modes was fitted using both the Lorenz three-parameter classical and four-parameter semiquantum models. Consequently, the modes were assigned as F1u(1) (144 cm−1), F1u(2) (284 cm−1), F1u(3) (330–468 cm−1), and F1u(4) (593–678 cm−1). The active modes were represented by linear combinations of symmetry coordinates that were obtained by group theory analyses. The Raman mode A1g, which has the highest wave number (812 cm−1) is dominated by the breath vibration of the MgO6 octahedron. The infrared modes F1u(2), that can be described as the inverted vibrations of Mg atoms in the MgO6 octahedron along the xi, yi, and zi axes have the most contributions to the microwave permittivity and dielectric loss.