This paper is devoted to investigating the existence and uniqueness of the
solution of Landau-Lifshitz-Bloch-Maxwell equation. The Landau-Lifshitz-Bloch-Maxwell equation, which fits well for a wide range of temperature, is
used to study the dynamics of magnetization vector in a ferromagnetic body.
If the initial data is in ($H$1, $L$2, $L$2), the existence of the global weak solution
is established. If the initial data is in ($H$$m$+1, $H$$m$, $H$$m$) ($m$ ≥ 1), the existence
and uniqueness of the global smooth solution are established.