  Let $B_{H}(t), t\geq [0,T], T\in(0,\infty)$ be the standard Multifractional
Brownian Motion(mBm), in this contribution we are concerned with the exact
asymptotics of \begin{eqnarray*}
  \mathbb{P}\left\{\sup_{t\in[0,T]}B_{H}(t)>u\right\} \end{eqnarray*} as
$u\rightarrow\infty$. Mainly depended on the structures of $H(t)$, the results
under several important cases are investigated.
