  We have constructed an isobar model for the $\eta$-photoproduction on the
proton in the energy region up to the photon lab energy $K_0 = 3$ GeV. The data
base involved into the fitting procedure includes precise results for the cross
section and for the $T$-asymmetry of the process $\gamma p\to\eta p$ near
threshold obtained at MAMI and ELSA as well as recent results for the
$\Sigma$-asymmetry and for the angular distribution measured at higher energies
in Grenoble and also more recent measurements performed at JLab for the photon
energies up to 2 GeV. The model includes twelve nucleon resonances:
$S_{11}(1535)$, $S_{11}(1650) $, $S_{11}(1825)$, $P_{11}(1440)$,$P_{13}(1720)$,
$D_{13}(1520)$, $D_ {15}(1675)$, $F_{15}(1680)$, $F_{17}(1990)$,$G_{17}(2190)$,
$G_{19} (2250)$, $H_{19}(2220)$, and the background consisting of the nucleon
pole term and the vector meson exchange in the $t$-channel. To explain the
observed energy dependence of the integrated cross section, two $s$ -wave
resonances, $S_{11}(1650)$ and $S_{11}(1825)$, have to be taken into account
along with the dominating $S_{11}(1535)$. The integrated cross section as well
as the angular distribution and $\Sigma$ asymmetry predicted by the model are
in good agreement with the data. Above the photon energy $K_0 = 2$ GeV, the
calculated cross section exhibits an appreciable dependence on the $\rho$- and
$\omega$-meson contribution, whose coupling with nucleons is not well defined.
Several versions of extending the model to higher energies are considered.
