  The role of the $\Lambda(1670)$ resonance in the $\gamma p \to K^+ \eta
\Lambda$ reaction near threshold is studied within an effective Lagrangian
approach. We perform a calculation for the total and differential cross section
of the $\gamma p \to K^+ \eta \Lambda$ reaction by including the contributions
from the $\Lambda(1670)$ intermediate state decaying into $\eta \Lambda$
dominated by $K^-$ and $K^{*-}$ mesons exchanges, the nucleon pole and
$N^*(1535)$ resonance decaying into $K^+ \Lambda$ dominated by exchanges of
$\omega$ and $K^-$ mesons. Besides, the non-resonance process and contact terms
to keep the total scattering amplitude gauge invariant are also considered.
With our model parameters, the total cross section of this reaction is of the
order of $1$ nanobarn at photon beam energy $E_{\gamma} \sim 2.5$ GeV. It is
expected that our model predictions could be tested by future experiments.
