Density functional theory based calculations are used to investigate the energetically and dynamically most stable structure for a crystalline unzipped graphene oxide (UGO) monolayer by considering parallel or anti-parallel dipolar structures. The O atom in the UGO monolayer induces electron excessive and deficient regions, which makes Li-ions selectively trapped in the electron deficient region. Apart from this, the periodic injection of O in graphene (C4O) opens a small band gap (0.6 eV) while keeps the Dirac cone. The adsorption of Li-ions makes it metallic by donating an extra electron to the UGO monolayer. The UGO monolayer can have a high Li storage capacity of 419 mAh/g and a typical anodic open circuit voltage range of 0.94-0.19 V. The energy barrier for Li migration is almost double of the pristine graphene, which results from the localized positive charge regions in the UGO monolayer.