We propose a six-fold photonic quasi-crystal fibre with a trapezoidal analyte channel based on surface plasmon resonance for the detection of high refractive index liquid analytes and numerically analyse its sensing performance for different liquid analyte refractive indices and heights using the finite element method. In contrast to the common D-shaped structure photonic crystal fibre, we design a trapezoidal analyte channel to investigate the role of the sample liquid height within the channel and discussed the feasibility of the fabrication process. We find that with various liquid analyte heights ratio of 20%, 25%, 30% and 50% of the maximum channel height, the proposed biosensor exhibits linear sensing performance with a maximum refractive index (RI) sensitivity of 4400 nm/RIU, 6100 nm/RIU, 8000 nm/RIU and 17000 nm/RIU respectively, for analytes RI range of 1.44 to 1.57, 1.41 to 1.51, 1.40 to 1.49 and 1.40 to 1.44. This sensor is suitable to detect various high RI chemicals, biochemicals and organic chemical samples. Owing to its simple structure of the proposed biosensor with promising linear sensing performance, we envisage that this biosensor could turn out to be a versatile and competitive instrument for the detection of high refractive index liquid analytes.