In this study, we have demonstrated the use of chemical vapour deposition (CVD) grown-graphene to develop a highly-ordered graphene-enzyme electrode for electrochemical biosensing. The graphene sheets were deposited on 1.00 mm thick copper sheet at 850 °C using acetylene (C2H2) as carbon source in an argon (Ar) and nitrogen (N2) atmosphere. An anionic surfactant was used to increase wettability and hydrophilicity of graphene; thereby facilitating the assembly of biomolecules on the electrode surface. Meanwhile, the theoretical calculations confirmed the successful modification of hydrophobic nature of graphene through the anionic surface assembly, which allowed high-ordered immobilisation of glucose oxidase (GOx) on the graphene. The electrochemical sensing activities of the graphene-electrode was explored as a model for bioelectrocatalysis. The bioelectrode exhibited a linear response to glucose concentration ranging from 0.2 to 9.8 mM, with sensitivity of 0.087 µA/µM/cm2 and a detection limit of 0.12 µM (S/N=3). This work sets the stage for the use of acetylene-sourced CVD-grown graphene as a fundamental building block in the fabrication of electrochemical biosensors and other bioelectronic devices.