Dielectric ceramics with low ε_r, high Q×f, and near-zero τ_f in the microwave bands are key materials used in fifth/sixth-generation (5G/6G) telecommunication, while the τ_f of most low-ε_r microwave dielectric ceramics is relatively negative. In this work, the first low-ε_r Ga-based ceramic SrGa₁₂O₁₉ with anomalous positive τ_f was reported, and the cause of positive τ_f, intrinsic polarization and loss mechanism were systematically studied. According to XRD and TEM, SrGa₁₂O₁₉ ceramic formed a pure hexagonal magnetoplumbite structure with the spinel block and the rock-salt block stacking along the crystallographic c-axis. When sintered at 1430 °C, it possessed the optimal microwave dielectric properties of low ε_r of 14.46, high Q×f of 64,705 GHz, and exceptional positive τ_f of +55.7 ppm/°C, along with a low linear thermal expansion coefficient (α_L) of 11.617 ppm/°C. The large positive deviation between ε_r and ε_r(C-M) of 45.31% resulted from the rattling effect of atoms in a rock-salt block. The unique positive τ_f (+55.7 ppm/°C) was governed by the rattling effect, resulting in a positive τ_αm of 8.489 ppm/℃ and a large negative τ_ε of −132.864 ppm/℃. The P-V-L chemical bond theory showed the greater contribution of the spinel block to f_i (52.95%), ε (55.15%), E (56.87%) and U (74.88%) than those of the rock-salt block. The intrinsic dielectric properties were analyzed using infrared reflectivity spectra. The favorable performances of SrGa₁₂O₁₉ ceramic indicated it is a novel τ_f compensator. This selection of compounds with different structural layer combinations provides a new idea for exploring excellent microwave dielectric ceramics.