A novel polyelectrolyte, poly[N-(1-one-butyric acid)benzimidazole] (PBI-BA), was synthesized and used to fabricate an amperometric hydrogen peroxide (H₂O₂) sensor. It was found that PBI-BA can be oxidized by H₂O₂ and produce a current response during electrochemical reduction. This mechanism was used to develop an enzyme-free H₂O₂ sensor. Under optimal experimental conditions, the sensor showed high reproducibility, selectivity and stability. The stability of the PBI-BA electrode after annealing at 100 °C was also studied. Interestingly, the sensitivity of the modified electrode was 15.2% higher than that without heat treatment. The sensor was sensitive toward H₂O₂ over a linear range from 6.2 μM to 5.0 mM with a detection limit of 3.1 μM. Because graphene sheets (Gs) suspend readily in the polyelectrolyte solution, a PBI-BA–Gs/Au electrode was also fabricated, improving the sensor's performance dramatically: this sensor detected H₂O₂ over a linear range of 2.5 μM to 5 mM, with a correlation coefficient of 0.998 (n = 5) and a sensitivity of 1056 μA mM⁻¹ cm⁻².