In electromagnetic metallurgy, argon is usually used as a power and carrier to blow desulfurizer and deoxidizer into liquid metal, so there is a problem of free movement of bubbles in liquid metal under a magnetic field environment. Flow past a fixed bubble as a special form of free movement, is the first step to study the problem of free movement. In this paper, the global linear stability analysis of the flow past a spherical bubble under the effect of a streamwise magnetic field is simulated by the finite element method. The response of the steady axisymmetric basic flow to the small perturbation of the independent time-azimuthal mode in the range of \mathitRe\leqslant 1000,N\leqslant 60 is discussed. Eight unstable stationary modes are found, and their neutral curves in the \mathitRe-N parameter plane or \mathitRe-Ha parameter plane are displayed. The results show that the stationary mode with azimuthal wave number m
= 1 leads to the first regular bifurcation, this mode has been widely confirmed as the most unstable mode in the flow past axisymmetric objects, which transforms the axisymmetric wake into a plane symmetric wake composed of a pair of opposite vortices. In addition, the results of the neutral curve show the effect of the magnetic field on the instability of the flow past the spherical bubble. The subsequent bifurcations are successively caused by the unstable modes of m
= 2, 3,..., 8, these bifurcations provide an important reference value for understanding the wake structure of the flow past a bubble in the magnetic field environment.