In this paper, a novel localized surface plasmon resonance (LSPR)-based micro-channel photonic crystal fiber (PCF) sensor is proposed. The LSPR-PCF sensor is designed with the three micro-channels, and the metal nanostraps and graphene are coated onto the PCF as the sensing elements. To realize high refractive index (RI) sensitivity, the influence of different plasmon materials, structure parameters, and graphene layers on the sensing performance of the LSPR-PCF sensor is investigated. The maximum wavelength sensitivity and amplitude sensitivity of the optimized LSPR-PCF sensor are up to 45800 nm/RIU and 1818RIU−1, respectively, when the RI changes from 1.35 to 1.42. Furthermore, the proposed LSPR-PCF sensor achieves the maximum figure of merit of 594.8, alone with a resolution of 2.18×10−6RIU. Because of its simple structure and excellent sensing performance, the proposed LSPR-PCF sensor has potential applications in biochemistry and environmental science.