This work presents a fiber Bragg grating (FBG) displacement sensor suitable for alternate positive and negative displacement measurement. When measuring alternating displacements, existing FBG displacement sensors need to pre-stretch to a certain state, thus the elastic element of the sensor will in a state of large deformation instead of the working 'zero deformation point'. The elastic element is easy to creep and lose its resilience, which will lead to inaccurate measurement. The FBG displacement sensor proposed in this work can overcome the above shortcomings. Through ingenious design, two pairs of 'FBG - cantilever - wedge shaped slider' structure are used for positive and negative displacement detecting respectively. When measuring the positive displacement, one cantilever beam with FBG is in a deformed state, while the other one is not deformed and provides temperature compensation. For negative displacement measurement, the situation is just reversed. Comprehensive performance tests have been carried out, and the experimental results demonstrate that the sensor possesses a measurement range of ±50mm and a sensitivity of 29.373 pm/mm. Furthermore, good micro-displacement measurement capability, creep resistance, and temperature compensation performance have also been demonstrated.