  The production of the $f_1(1285)$ resonance in the reaction of $\gamma p
\rightarrow f_1(1285) p$ is investigated within a Regge-effective Lagrangian
approach. Besides the contributions of the $t$-channel $\rho$ and $\omega$
trajectories exchanges, we also take into account the contributions of
$s/u$-channel $N(2300)$ terms, $s/u$-channel nucleon terms, and the contact
term. By fitting to the CLAS data, we find that the $s$-channel $N(2300)$ term
plays an important role in this reaction. We predict the total cross section
for this reaction, and find a clear bump structure around $W=2.3$ GeV, which is
associated with the $N(2300)$ state. The reaction of $\gamma p \to f_1(1285) p$
could be useful to further study of the $N(2300)$ experimentally.
