  In this article, we bring in Landau-Lifshitz-Bloch(LLB) equation on
$m$-dimensional closed Riemannian manifold and prove that it admits a unique
local solution. In addition, if $m\geqslant3$ and $L^{\infty}-$norm of initial
data is sufficiently small, the solution can be extended globally. Moreover, if
$m=2$, we can prove that the unique solution is global without assuming small
initial data.
