  In this paper we consider the global well-posedness of compressible
magnetohydrodynamic system in $\R^d$ with $d\geq2$, in the framework of the
critical Besov spaces. We can show that if the initial data, the shear
viscosity and the magnetic diffusion coefficient are small comparing with the
volume viscosity, then compressible magnetohydrodynamic system has a unique
global solution.
