Structural evolution of Li(3-3x)M4xNb(1-x)O4 (M = Mg,Zn; 0 <= x <= 0.9) and microwave dielectric properties of Li(3-3x) Mg4xNb(1 x)O4 have been studied by X-ray diffraction, scanning electron microscopy, Raman spectra, infrared reflectivity (IR) fitting, and microwave resonant measurement in this work. The crystal symmetry changed from the ordered cubic Li3NbO4 (I-43m, x = 0) into disordered cubic phase (Fm3m) when 0.01 <= x < 1/3 for the Mg-doped samples. An intermediate compound of Li3Mg2NbO6 (SG:Fddd) with orthorhombic structure formed at x = 1/3 composition. MgO secondary phase appeared in addition to Li3Mg2NbO6 phase in the x > 1/3 compositions, and its content increased with the further increase of x. Short-range cation ordering was confirmed to be present in the cubic phase by Raman analysis. Mixture of Li3NbO4 and ZnO phases was observed in the whole composition range for the ZnO-added samples. For the Mg-doped samples, the dielectric constant increased slightly with x increasing up to x = 1/3 and decreased with the further increase of x. The Q x f value increased greatly with the increasing x and saturated within the composition range of 0.1 <= x < 1/3. Further increasing x resulted in a decrease in Q x f value. All samples exhibited negative tau(f) value. Minimum tau(f) value of -22 ppm/degrees C was obtained at x = 1/3. The IR reflection spectra of the x = 0, 0.2, and 1/3 samples were analyzed by Kramers-Kroning analysis and classical oscillator model simulation. The dielectric properties were extrapolated down to the microwave range using the classical oscillator model for fitting the dielectric function. The calculated dielectric constants were in agreement with the experimental ones, whereas, the calculated Q x f values showed a reverse varying trend compared with the experimental data.