The state and dynamic behaviour of the Li+ ions in Li1-2xTi2-xMgxP3O12 fast ionic conductor system have been investigated with Li-7 solid-state NMR techniques. Two activation energy of Li- ions motion in the different temperature range and two mangnetic inequivalent Li nuclei are indentified from NMR results. The mechanism of Li+ ions transport in this system are discussed based on the temperatures dependence of Li NMR line shape and Li-7 nucleus spin-lattice relaxation time T-1.