Development of lithium ion batteries employing solid polymer electrolytes as electrolyte material has led to efficient energy storage and usage in many portable devices. However, due to a few drawbacks like lower ionic conductivity of solid polymer electrolytes (SPEs), studies on SPEs for improvement in conductivity still have a good scope. In the present paper, we report the conductivity studies of a new SPE with low molecular weight poly ethylene glycol (PEG) as host polymer in which a salt with larger anion Lithium trifluro methane sulphonate (LTMS). XRD studies have revealed that the salt completely dissociates in the polymer giving a good stable electrolyte at lower salt concentration. Conductivity of the SPEs has been studied as a function of temperature and we reiterate that the conductivity is a thermally activated process and follows Arrhenius type behavior.