During directional solidification of binary alloy mixtures, instability in the solid/liquid interface appears due to constitutional undercooling. As a result of this instability, a reactive porous medium, namely mushy layer, is formed, and it separates the liquid phase from the solid phase completely. The intrinsic structure of the mushy layer is of fine-scale dendritic crystal that shelters solute in the interstitial fluid. In a gravitational field, the rejection of lighter solute components from an advancing solidification front brings about unstable density gradient. Ensuing convective motions in the mush are driven by a density difference. The convection can change the solid matrix of the mushy layer. Hence, the dynamic response of the mushy layer is driven by interaction among heat transfer, solute transport and convection. As a contactless control tool, external magnetic field can change the heat and solute transport, which has a significant effect on the phase change process. Therefore, when magnetic field, thermal diffusion, solute transport and buoyancy convection are considered simultaneously in the phase transformation process, the mechanism of mushy region will become more complex and interesting. In this paper, the effect of external magnetic field on the stability of mushy layer during binary alloy solidification is studied. The coupling effects of magnetic field, temperature field, concentration field and convection are considered in the model. Including the direct mode and the oscillation mode, the resulting dispersion relation reveals the influence of magnetic field on the stability of mushy layer through linear stability analysis. It is found that the Lorentz force can reduce the instability effect which is caused by buoyancy convection. In the oscillation mode, an external magnetic field brings about a stabilizing effect on the mushy layer, but in the direct mode, the effect of external magnetic field on stability of the mushy layer is uncertain. In conclusion, the finding in this paper provides an important theoretical reference for improving products quality by applying an external magnetic field in the metals processing industry.