A highly tunable bandgap-guiding microstructured polymer optical fiber (mPOF) is designed by infiltrating the cladding air holes with a liquid crystal. Bandgap is blue shifted as temperature is increased. A high thermal tuning sensitivity of -5.5 nm/℃ is achieved at the long-wavelength edge of the bandgap. Mode properties and effective mode area of the fundamental mode are investigated by using the full-vector finite element method. The designed fiber has a large effective area and high power transmission coefficient between the index guiding modes and the bandgap guiding modes. Our results provide theoretical references for applications of mPOF in sensing and tunable fiber-optic devices.