In the quest for safer energy storage devices, researchers have been diligently exploring solid polymer electrolytes in recent years. This study explores the development of solid biopolymer electrolytes through solution casting, utilizing cellulose acetate blended with various concentration of LiBr. Inclusion of LiBr salt makes the membrane amorphous, confirmed using XRD. Cellulose acetate–LiBr complexation is confirmed by FTIR. The thermal stability of membranes is analyzed using TGA and DSC. From DSC, the low glass transition temperature (51 °C) of the membrane 1 g cellulose acetate with 0.6 wt.% LiBr leads to the flexibility of the membrane which helps to increase the Li-ionic conductivity. Thermal stability of the highest Li-ionic conducting membrane CALB3 indicates that if the battery is constructed with this membrane, it will be thermally stable up to 60 °C. The membrane with composition 1 g cellulose acetate with 0.6 wt.% LiBr is confirmed as the highest Li-ion-conducting membrane with ionic conductivity value 3.16 × 10−3 S cm−1 among all prepared membranes. The electrochemical stability window of the highest Li-ion-conducting membrane is 2.2 V given by linear sweep voltammetry. The membrane CALB3 having high Li-ion conductivity is used as electrolyte to construct primary Li-ion battery. The primary Li-ion battery shows an open-circuit voltage of 1.68 V and the performance of battery for various loads has been measured. Rechargeable Li-ion battery (coin cell) is constructed using the high Li-ion-conducting membrane as electrolyte. The constructed coin cell behaves like a pseudocapacitor.