We demonstrate the fabrication of a high-sensitivity magnetic field sensor based on the packaged long-period fiber grating (LPFG) with magnetic fluid. The transmission spectra and the surrounding refractive index (SRI) characteristics of the LPFGs near the dispersion turning point (DTP) were investigated theoretically and experimentally. We have studied the influence of mode order and wavelength separation at DTP on the SRI sensitivity of the DTP-LPFG. The experimental results are consistent with the simulation. The LP0,10 mode has the highest SRI sensitivity of 1956.4 nm/RIU in the range of 1.333-1.435 when the wavelength separation at DTP is 89.1 nm. The sensor achieves a magnetic field sensitivity of 1.9 nm/mT in the magnetic field intensity range of 0-20.5 mT, which indicates that the sensor can be used as a high-sensitivity magnetic field sensor.