In this paper, a new fiber Bragg grating (FBG) sensor exploiting microwave photonics filter technique for transverse load sensing is firstly proposed and experimentally demonstrated. A two-tap incoherent notch microwave photonics filter (MPF) based on a transverse loaded FBG, a polarization beam splitter (PBS), a tunable delay line (TDL) and a length of dispersion compensating fiber (DCF) is demonstrated. The frequency response of the filter with respect to the transverse load is studied. By detecting the resonance frequency shifts of the notch MPF, the transverse load can be determined. The theoretical and experimental results show that the proposed FBG sensor has a higher resolution than traditional methods based on optical spectrum analysis. The sensitivity of the sensor is measured to be as high as 2.5 MHz/N for a sensing fiber with a length of 18mm. Moreover, the sensitivity can be easily adjusted.