Through Faraday- effect, dual- polarization fiber grating laser based on magnetic field sensor is demonstrated. However, the sensitivity to magnetic field of such sensor is dependent on the initial beat frequency of the laser. Therefore, the relationship between the beat frequency and the sensitivity of such sensor is studied. Theoretical and experimental results show that the dependence of the sensitivity on the beat frequency is nonlinear. Moreover, the sensitivity increases with the decrease of beat frequency. However, there is an upper limit of this sensitivity which is determined by Verdet constant. By lowering the beat frequency to 2 MHz, the maximum sensitivity about 43 Hz/mT to magnetic field is achieved for a dual- polarization fiber grating laser inscribed on an erbium doped fiber. It also shows that the beat frequency is dependent on the polarization of the 980 nm pump. Therefore, dynamical tuning of the sensitivity optically can be demonstrated by tuning the polarization of the 980 nm pump.