The need for flexible biosensors has increased because of their potential applications for point-of-care diagnosis and wearable biosensors. However, flexible biosensors have low sensitivity due to the flexibility of the electrode, and their fabrication involves complex processes. To overcome these limitations, a flexible electrochemical enzyme biosensor was developed in this study by immobilizing an enzyme on the flexible polymer electrode modified with a gold/MoS2/gold nanofilm. The fabrication process involved sputter deposition of gold, spin coating of MoS2, and sputter deposition of gold on the flexible polymer electrode (commercially available Kapton® polyimide film). The flexible glucose biosensor was made by immobilization of glucose oxidase on a flexible electrode by using a chemical linker. The detection limit for glucose was estimated to be 10 nM, which indicates more sensitivity as compared with a previously reported flexible glucose sensor. This sensitivity is due to the facilitation of electron transfer by MoS2. The flexure extension of this biosensor was estimated at 3.48 mm, which is much higher than that of the rigid sensor using a gold-coated silicon electrode (0.09 mm), according to measurements with a micro-fatigue tester. The proposed flexible biosensor composed of the enzyme/gold/MoS2/gold nanofilm on the polymer electrode can be used as a flexible sensing platform for developing wearable biosensing systems because of its high sensitivity, high flexibility, and simple fabrication process.