To address the issues of low mechanical strength and weak robustness in the tapered waist region of existing tapered fiber-coupled microtube cavity whispering gallery mode (WGM) sensors, a microtube cavity refractive index sensor based on a wedge-shaped fiber (WSF) is proposed. By utilizing the evanescent field excited from the WSF end-face to couple with the microtube cavity and form WGM, a theoretical model is established using the finite-difference time-domain (FDTD) method. The effects of wedge angle, wall thickness, and microtube cavity outer diameter on refractive index sensing characteristics are thoroughly investigated. The simulation results show that when the wedge angle is 20°, the tube wall thickness is 1 μm, and the microtube outer diameter is 110 μm, the sensor achieves a refractive index sensitivity of 326.5 nm/RIU, a quality factor of 3.236× 10³, and a resolution of 6.12×10^-5 RIU. When used for glucose concentration detection, the sensor demonstrates a sensitivity of 0.085 nm/mM and a resolution of 0.23 mM.