It is the truth that many large-scale engineering structures have large deformation while they are still functional. Based on the bending loss characteristics of an optical fiber, we present a large range and linear sensor with simple construction for displacement measurement. The linear relationship between the measured displacement and the bending loss of an optical fiber is proved theoretically, and its expression is derived. A series of calibration experiments and performance tests are conducted. The experimental results show that the sensor is characterized by a wide measurement range of 0--200 mm, a sensitivity of 0.1668 dB·mm ^-1, a minimum displacement resolution of 0.06 mm, a repeatability error of 0.26%, and a hysteresis error of 2.22%. The designed sensor can be used for the crack detection and the continuous monitoring for large-scale engineering structures and has a promising application prospect.