The solid electrolyte Li1+2xMgxTi2-xP3O12 compounds were synthesized by a solid state reaction. The ceramic samples were sintered for 0.2, 0.5, 1 and 3 h and studied by X-ray and complex impedance spectroscopy in the frequency range 10 Hz-1.2 GHz in the temperature range 300-600 K. Two regions of relaxation dispersion were found, the dispersions were related to the fast Li+ ion transport in the bulk and grain boundaries. Varying of the sintering time affects the density, values of grain boundary conductivity (sigma(gb)), its activation energy (DeltaE(gb)) and relaxation frequency (f(gb)). The activation energy (DeltaE(b)) of bulk conductivity (sigma(b)) and activation energy (DeltaE(f)) of relaxation frequency (f(b)) in the bulk are the same. That can be attributed to the fact that the temperature dependence of the bulk conductivity is caused only by the mobility of the fast Li+ ions, while a number of charge carriers remains constant with temperature.