In this work, we theoretically propose an optical biosensor (consists of a BK7 glass, a metal film, and a graphene sheet) based on photonic spin Hall effect (SHE). We establish a quantitative relationship between the spin-dependent shift in photonic SHE and the refractive index of sensing medium. It is found that, by considering the surface plasmon resonance effect, the refractive index variations owing to the adsorption of biomolecules in sensing medium can effectively change the spin-dependent displacements. Remarkably, using the weak measurement method, this tiny spin-dependent shifts can be detected with a desirable accuracy so that the corresponding biomolecules concentration can be determined.