Consider the standard first-passage percolation on ${\Z}^d$, $d\geq 2$.
Denote by $\phi_{0,n}$ the face--face first-passage time in $[0,n]^d$.
It is well known that
\[
\lim_{n\rightarrow \infty} {\phi_{0,n}\over n}=\mu(F)
\qquad \mbox{a.s. and in } L_1,
\]
where $F$ is the common distribution on each edge.
In this paper we show that the upper and lower tails of $\phi_{0,n}$
are quite different when $\mu(F)>0$. More precisely, we can show
that for small $\varepsilon>0$, there exist constants $\alpha(\varepsilon, F)$
and $\beta (\varepsilon, F)$
such that
\[
\lim_{n\rightarrow\infty}{-1\over n}
\log P \left( \phi_{0,n}\leq n(\mu -\varepsilon) \right)
= \alpha (\varepsilon, F)
\]
and
\[
\lim_{n\rightarrow\infty}{-1\over n^d}
\log P \left(\phi_{0,n}\geq n(\mu +\varepsilon) \right)= \beta (\varepsilon, F).
\]