In order to investigate the impact of an external electric field on the sensitivity of β-HMX explosives, we employ first-principles calculations to determine the molecular structure, dipole moment, and electronic properties of both β-HMX crystals and individual β-HMX molecules under varying electric fields. When the external electric field is increasing along the [100], [010], and [001] crystallographic directions of β-HMX, the calculation results indicate that an increase in the bond length (N1-N3/N1'-N3') of the triggering bond, an increase in the main Qnitro (N3, N3') value, an increase in the minimum surface electrostatic potential, and a decrease in band gap all contribute to a reduction in its stability. Among these directions, the [010] direction exhibits the highest sensitivity, which can be attributed to the significantly smaller effective mass along the [010] direction compared with the [001] and [100] directions. Moreover, the application of an external electric field along the Y direction of the coordinate system on individual β-HMX molecules reveals that the strong polarization effect induced by the electric field enhances the decomposition of the N1-N3 bonds. In addition, due to the periodic potential energy of β-HXM crystal, the polarization effect of β-HMX crystal caused by an external electric field is much smaller than that of a single β-HXM molecule.