Here, we propose a novel fiber-optic sensor capable of simultaneous measurements of strain and temperature by using a long-period fiber grating (LPFG) inscribed on a twisted high-birefringence photonic crystal fiber (HBPCF) as a sensor head. The sensor head was fabricated by scanning CO2 laser pulses to one side of the twisted HBPCF using a line-by-line technique. The LPFG written on the twisted HBPCF (referred to as a THBPC-LPFG) exhibits two different resonance bands, obtained at two orthogonal input polarization states, with multiple attenuation dips within each band. Two attenuation dips, each of which was selected in each resonance band, were utilized as sensor indicators. For these two indicator dips designated as Dips 1 and 2, their strain and temperature responses were examined in a strain range of 0–1953 με with a step of 217 με and in a temperature range of 35–95 °C with a step of 10 °C. At a fixed room temperature (25 °C), that is, without any temperature changes, the strain sensitivities of Dips 1 and 2 were measured to be approximately −0.99 and −1.29 pm/με, respectively. Similarly, the temperature sensitivities of Dips 1 and 2 were measured and found to be ~7.14 and ~10.07 pm/°C without the applied strain, respectively. Owing to their linear and independent responses to strain and temperature, strain and temperature changes applied to the THBPC-LPFG can be simultaneously estimated from the measured wavelength shifts of the two indicator dips (i.e., Dips 1 and 2) using their predetermined strain and temperature sensitivities. From the repetitive simultaneous measurements of the applied strain and temperature, the rms deviations of the measured strain and temperature were evaluated as 20.2 µε and 1.78 °C, respectively. The experimental results prove that the THBPC-LPFG can be employed as a cost-effective sensor head for the simultaneous measurements of strain and temperature.