Abstract: The argon blowing refining process in electromagnetic metallurgy involves the problem of free movement of bubbles in liquid metal under magnetic field environment. In order to explore the influence of magnetic field on the structure of bubble wake, linear stability analysis is used to study the wake instabilities of the flow past a fixed bubble with different aspect ratios under the effect of a streamwise magnetic field. The response of the steady axisymmetric basic flow for bubble aspect ratio χ = 2.5 to the small perturbation of the independent time-azimuthal mode is discussed, and the neutral curves of unstable modes in the Re-N parameter plane or Re-Ha parameter plane are displayed, results show that big aspect ratio can easily excite high-order unstable modes with azimuthal wavenumbers m > 1 under strong magnetic field. Furthermore, the influence of magnetic field intensity on the first bifurcation of flow past a bubble in the area of aspect ratio 0.5≤χ≤2.5 is discussed, results show that the critical Reynolds number Re_c of the wake instability of bullet shape bubble of χ = 0.5 is always higher in the whole field range (interaction number N≤100) than that of oblate spheroid bubble χ≥1. However, in the range of 1≤χ≤2.5, when the magnetic field intensity increases to a certain value, the bifurcation of flow past a bubble with small aspect ratio appears earlier than that with large aspect ratio, indicating that the strong magnetic field altered the more stable properties of the wake for small aspect ratio bubble. By integrating the neutral curves of various unstable modes and aspect ratios, it can be concluded that weak magnetic field has a stabilizing effect on the wake structure of flow past a bubble, while strong magnetic field promotes wake instability, and the much stronger magnetic field exhibits a stabilizing effect again.