The transfer matrix method is developed to probe bianisotropic biomolecules via a Kretschmann configuration surface plasmon resonance (SPR) sensor. This method employs wave vectors and 4 × 4 transfer matrices derived by using anisotropic and magnetoelectric coupling constitutive relations. The transfer matrices relate four eigenstates and trace four transverse field components through the multilayer to account for cross-polarization coupling due to the chirality of the biomolecule layer. The validity of the method is confirmed by means of numerical results. It is shown that cross-polarized reflection waves are enhanced around the SPR angle, as the water solution and bianisotropic biomolecules to be detected are placed in contact with the graphene layer of the sensor. The effects of optical activity and bianisotropy on the SPR sensor are investigated. This work enriches the transfer matrix theory for SPR sensors to detect the chirality parameter of bianisotropic chiral material, and may lead to a better design of SPR sensors against the chirality parameter variation.