A Fabry-Pérot interferometer (FPI) strain sensor with low-temperature cross-sensitivity is prepared by a simple, cost-effective, and safe process. The sensor is fabricated by splicing two segments of the single-mode fiber and several arc discharges to form a unique circular bubble and a thin wall. The thin air-bubble wall deforms more easily under stress due to the good stress concentration ability of the tapered structure, resulting in a high strain sensitivity of 10.78 pm/µε. The temperature sensitivity of the sensor is 1.24 pm/°C and the temperature cross-sensitivity is 0.115 με/°C in the temperature range of 25 to 200 °C, which reduces the temperature-induced measurement error. The experimental results show that the sensor with good stability and repeatability has large commercial potential in measuring strain in complex environments.