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 database involved into the fitting procedure includes precise results for the cross-section and for the T-asymmetry of the process gammap --> etap 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 and 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.