Entrapment is one of the major approaches for enzyme immobilization; however, it suffers a few critical drawbacks including leakage and high mass transfer resistance to substrates. To address these challenges, herein we report on a new facile and effective enzyme entrapment platform using a special cationic polymer, poly(2-(dimethylamino)ethyl methacrylate) (MADQUAT) on a single-wall carbon nanotube and reduced graphene oxide (SWCNT–rGO) nanohybrid thin film. To demonstrate this new approach, alcohol dehydrogenase (ADH) is employed as a model enzyme for the entrapment toward the design of an efficient electrochemical biosensor for the detection of ethanol. MADQUAT possesses strong electrostatic affinity with various negatively charged biomolecules; and our FTIR study has shown that there are no structural changes in the enzyme following the entrapment, with an excellent secondary structure association (r = 0.92). Our electrochemical measurements have shown that the entrapped ADH exhibits high ability to exchange electrons in the presence of the NAD⁺/NADH cofactor and that the SWCNT–rGO nanohybrid significantly enhances the biocatalytic activity of the immobilized ADH and the electrochemical oxidation of NADH in comparison with either SWCNTs or rGO. The ethanol biosensor developed in this study exhibits a fast response, wide linearity range, high sensitivity (26.27 μA mM⁻¹ cm⁻²), remarkable low limit of detection (0.16 μM), high selectivity and high stability. The optimized biosensor has been further tested with real samples including wine, beer and blood alcohol, showing promising analytical and biomedical applications.