  We study the $\eta$-photoproduction focusing on the new nucleon resonance
which was observed at $\sqrt{s}=1675$ MeV with a narrow decay width ($\sim 10$
MeV) in the recent GRAAL experiment. Using an effective Lagrangian approach, we
compute differential cross sections for the $\eta$-photoproduction. In addition
to $N^*(1675)$, we employ three other nucleon resonances, i.e. $N^*(1535)$,
$N^*(1650)$ and $N^*(1710)$, and vector meson exchanges which are the most
relevant ones to this reaction process. As a result, we can reproduce the GRAAL
data qualitatively well and observe obvious isospin asymmetry between the
transition magnetic moments of $N^*(1675)$: $\mu_{\gamma nn^*}\gg\mu_{\gamma
pp^*}$.
