In this paper, a method to improve the precision of prism-coupler-based surface plasmon resonance (SPR) sensors using weak-value amplification (WVA) is presented. A general theory model to describe the post-selected SPR sensing system is established and the polarization-dependent amplitude and phase evolutions induced by the SPR are regarded as the weak interactions in the WVA formalism. As a consequence of WVA, the detected signal can be enhanced with respect to the technical noise which is dependent on the post-selected light intensity. The precision of our method reaches 2.9 × 10-7RIU, which is improved nearly one order of magnitude compared to the conventional sensing technique.