A new type of highly sensitive near-infrared birefringent six-core photonic crystal fibre sensor using surface plasmon resonance (SPR) is proposed. By using the full-vector finite element method, the impacts of the fibre parameters on the wavelength sensitivity and amplitude sensitivity are numerically studied. The numerical results indicate that, benefiting from the high birefringent multi-core fibre structure, an average sensitivity of 8083 nm/refractive index unit (RIU) within the wavelength range from 1.532 to 2.02 µm is achieved when the analyte refractive index (RI) lies in (1.372, 1.432). Moreover, the maximum amplitude sensitivity is as high as 226 RIU−1 if the analyte RI is adjusted from 1.372 to 1.382. In consideration of its excellent sensing performance, the proposed SPR multi-core PCF sensor can be applied in environmental, food safety, and (bio)chemical detection.