According to the principle of Faraday effect,the magnetic field can be measured with the polarization dependent loss (PDL) of the fiber Bragg gratings FBG. The polarization of light is changed by the liner birefringence existing in(FBG). The intrinsic PDL in the different structure gratings is simulated and measured,and the validity of the result is proved. The change of the state of polarization with the magnetic field and birefringence is theoretically analyzed and simulated by using the Jones matrix. The influences of liner birefringence and polarizing angle on the measurement system are compared. The peak of PDL and the cross sensitivity of the system vary with different polarizing angle. The linear relation between the magnetic field and the peak of PDL is not affected by these factors.