||We investigate eta photoproduction off the neutron target, i.e., gamma n -> eta n, employing an effective Lagrangian method combining with a Regge approach. As a background, we consider nucleon exchange in the s-channel diagram and rho- and omega-meson Regge trajectories in the t channel. The role of nucleon resonances given in the Review of Particle Data Group in the range of W approximate to 1500-2100 MeV and the narrow nucleon resonance N(1685; 1/2(+)) is extensively studied. The numerical results of the total and differential cross sections, double polarization observable E, helicity-dependent cross sections sigma(1/2), sigma(3/2), and the Legendre coefficients of the angular distributions for sigma(1/2), sigma(3/2) are found to be in qualitative agreement with the recent A2 experimental data. The predictions of the beam asymmetry are also given.