A novel magnetic field sensor based on a chirped effect of Fiber Bragg Grating(FBG) was proposed. The relationship between the magnetic induction intensity and the variable bandwidth of reflection spectrum of the FBG was derived. The working principle of the sensor was introduced.Firstly, the magnetic force from an energized spiral coil was applied to a disc-shaped soft iron in a magnetic field to make the rectangular cantilever beam deformed, which resulted in the bandwidth change of the reflection spectrum of FBG that was mounted at a side of the cantilever. As mentioned above, the magnetic induction intensity could be obtained by measuring the variable bandwidth of the reflection spectrum of the FBG with a spectral analyzer. The experiments show when the optical spectral analyzer is with a resolution of 0.001 nm, the measuring range of the sensor is up to 6-70 mT. Experimental results demonstrate that the variable bandwidth of the reflection spectrum of FBG is not sensitive to temperature change. The 3 dB bandwidth change is less than 8 nm when the temperature changes from 0 to 45 ℃, which is consistent with theoretical value well. The sensor scheme is feasible and practical.