In this work we report a proton (H-1) and lithium (Li-7) NMR lineshape and spin-lattice relaxation time investigation of this polymer electrolyte obtained from the polymerization of ethylene glycol and citric acid with lithium salt. The Li-7 data indicates that the lineshape and spin-lattice relaxation is affected by the coupling of its quadrupolar moment to the surrounding electric field gradients. The activation energy for the lithium motion extracted from the Li-7 relaxation data is 0.23 eV. The dynamics parameters obtained from the NMR data indicate that the lithium mobility in the EG:CA:LiCIO4 is comparable to those found in polymer gel electyrolytes and in plasticized polymer electrolytes.