Herein a novel strategy for the construction of an amperometric biosensor for highly sensitive and selective determination of glucose is described. The biosensor is made of a biocomposite membrane of glucose oxidase (GOx) and an Os(bpy)2 (bpy=2,2′-bipyridine)-based anionic redox polymer (Os-RP) mediator. The biosensor is fabricated through the co-immobilization of GOx and the Os-RP on the surface of a glassy carbon electrode by a simple one-step chemical crosslinking process. The crosslinked Os-RP/GOx composite membrane shows excellent catalytic activity toward the oxidation of glucose. Under optimal experimental conditions, a linear correlation between the oxidation current of glucose in amperometry at 0.25 V (vs. Ag/AgCl) and glucose concentration up to 10 mM with a sensitivity of 16.5 μA mM−1 cm−2 and a response time <5 s. Due to the presence of anionic sulfonic acid groups in the backbone of the redox polymer, the biosensor exhibits excellent selectivity to glucose in the presence of ascorbic acid and uric acid. The low hydrophobicity of the composite membrane also effectively retards the transport of molecular oxygen within the membrane.