We investigate the eta photoproduction using the effective Lagrangian approach at the tree level. We focus on the new nucleon resonance N*(1675), which was reported by the GRAAL, CB-ELSA and Tohoku LNS, testing its possible spin and parity states theoretically (J^P=1/2^+-,3/2^+-). In addition, we include six nucleon resonances, D_13(1520), S_11(1535), S_11(1650), D_15(1675), P_11(1710), P_13(1720) as well as the possible background contributions. We calculate various cross sections including beam asymmetries for the neutron and proton targets. We find noticeable isospin asymmetry in transition amplitudes for photon and neutron targets. This observation may indicate that the new resonance can be identified as a non-strangeness member of the baryon antidecuplet.