A way to measure displacement with chirp fiber grating is proposed based on beam cantilever. When the strain is acting on the cantilever beam, the reflection spectrum of the chirp grating pasted on the cantilever beam is compressed and the displacement can be measured according to the bandwidth of the reflection spectrum. The structure resolves the cross sensitization of the temperature to the displacement measurement. The variation in temperature results in the displacement of the whole reflection spectrum but does not change the bandwidth. The test result shows that this sensor has high accuracy, well linearity and repeatability.