  In this paper, we show that the first passage time in the frog model on
$\Z^d$ with $d\geq 2$ has a sublinear variance. This implies that the central
limit theorem does not holds at least with the standard diffusive scaling. The
proof is based on the method introduced in \cite{BRo, DHS} combining with a
control of the maximal weight of paths in locally dependent site-percolation.
We also apply this method to get the linearity of the lengths of optimal
paths..
