Li2SO4 have been synthesized from lithium sulphate monohydrate by melting at 880 °C and slow cooling. The XRD results indicates that the melt cooled Li2SO4 is crystallized to monoclinic structure. The AC conductivity (σac) and dielectric relaxation (tan δ) have been measured within the temperature range 170–250 °C and frequency range 100 Hz–120 kHz, respectively. The DC conductivities are conveniently extracted from σac (typical values ∼2 × 10−7 and ∼2 × 10−6 S/cm at 200 and 250 °C, respectively) and are fitted to linear Arrhenius plot. The slope of this linear plot leads to an activation energy of 1.10 eV. It is found that the conduction in Li2SO4 is mainly through Li+. Further, we carried out first principles calculations and obtained the structural and bonding properties of Li2SO4. From band structure, Li2SO4 is found to be a wide band gap insulator with a band gap of 6.1 eV. The partial density of states reveals the finite states of Li+ near to Fermi level, which limits its use of full capacity. This indicates a kinetic barrier for Li ions and electrons ambipolar diffusion.