We propose and demonstrate a novel surface plasmon resonance (SPR)-sensing approach by using the fundamental mode beam based on a twin-core fiber (TCF). Although normally in a fiber SPR sensor, a multimode fiber (MMF) has often been used to improve the coupling efficiency; for improving fiber SPR sensor sensitivity, single-mode beam is optimal. We provide a novel method to employ the single (fundamental)-mode beam to SPR sense based on the TCF. We grind the TCF tip to be a frustum wedge shape, and plate a 50-nm sensing gold film on the end face, and two 500-nm reflected gold films on the side faces of the wedge tip. By using this new configuration, we reduce the mode noise effectively and get a high testing sensitivity (the testing highest sensitivity reaches to 6463 nm/RIU). This SPR probe can be applied in a microfluidic chip and monitors the refractive index (RI) charges of the flow liquid in the microfluidic channel in real-time. The probe successfully monitors the refractive index of liquid ranged from 1.3333 to 1.3706, and the average sensitivity reaches to 5213 nm/RIU in the solution, which is much higher than most multimode SPR systems.