A low-cost and robust extrinsic Fabry-Perot interferometer (EFPI) based optical fiber displacement sensor with a wide measurement range, up to cm level, is reported in this paper. A gold-coated reflective mirror fixed inside the metal shell of the sensor, together with the endface of a single mode fiber form a Fabry-Perot cavity. The optical fiber is supported and oriented by a fiber ceramic ferrule, and the sensor is packaged and protected by a metal shell. A triangle geometry based displacement transfer mechanism is employed in the constructed sensor which makes the sensor capable of measuring wide-range displacement, and this triangle geometry based structure allows the measurement range of the sensor to be flexibly adjusted. When the measurement handgrip of the sensor experiences a displacement, the cavity length will change due to the triangle geometry design. By tracking the change in the reflection spectrum, the displacement can be determined. The experimental results show that a displacement measurement sensitivity of 42.68 nm/μm (change in EFPI cavity length/displacement magnitude) over a measurement range of 2.0 cm was achieved by the constructed prototype sensor. The present wide-range displacement sensor with low cost, high robustness has a great potential in the chemical-oil industry, the construction industry.