  The semisimple Frobenius manifolds related to the Hurwitz spaces
$H_{g,N}(k_1, ..., k_l)$ are considered. We show that the corresponding
isomonodromic tau-function $\tau_I$ coincides with $(-1/2)$-power of the
Bergmann tau-function which was introduced in a recent work by the authors
\cite{KokKor}. This enables us to calculate explicitly the $G$-function of
Frobenius manifolds related to the Hurwitz spaces $H_{0, N}(k_1, ..., k_l)$ and
$H_{1, N}(k_1, ..., k_l)$. As simple consequences we get formulas for the
$G$-functions of the Frobenius manifolds ${\mathbb C}^N/\tilde{W}^k(A_{N-1})$
and ${\mathbb C}\times{\mathbb C}^{N-1}\times\{\Im z >0\}/J(A_{N-1})$, where
$\tilde{W}^k(A_{N-1})$ is an extended affine Weyl group and $J(A_{N-1})$ is a
Jacobi group, in particular, proving the conjecture of \cite{Strachan}. In case
of Frobenius manifolds related to Hurwitz spaces $H_{g, N}(k_1, ..., k_l)$ with
$g\geq2$ we obtain formulas for $|\tau_I|^2$ which allows to compute the real
part of the $G$-function.
