Laser-induced graphene (LIG) has recently received increasing attention due to its simple fabrication and low cost. This study reports a flexible laser-induced graphene-based electrochemical biosensor fabricated on a polymer substrate by the laser direct engraving process. For this purpose, a 450 nm UV laser was employed to produce a laser-induced graphene electrode (LIGE) on a polyimide substrate. After the laser engraving of LIGE, the chitosan-glucose oxidase (GOx) composite was immobilized on the LIGE surface to develop the biosensor for glucose detection. It was observed that the developed LIGE biosensor exhibited good amperometric responses toward glucose detection over a wide linear range up to 8 mM. The GOx/Chitosan-modified LIGE biosensor showed high sensitivity of 43.15 µA mM−1 cm−2 with a detection limit of 0.431 mM. The interference studies performed with some possible interfering compounds such as ascorbic acid, uric acid, and urea exhibited no interference as there was no difference observed in the amperometric glucose detection. It was suggested that the LIGE-based biosensor proposed herein was easy to prepare and could be used for low-cost, rapid, and sensitive/selective glucose detection.