  The near threshold $\pi^- p \to \eta n$ reaction is studied within an
effective Lagrangian approach and the isobar model. By considering the
contributions from $s$- and $u$-channel nucleon pole and $N^{*}(1535)$
resonance, the total and differential cross sections of the $\pi^- p \to \eta
n$ reaction near threshold are calculated. Our theoretical results can fairly
reproduce the current experimental data. It is also shown that while the
center-of-mass energy lies in the range from the reaction threshold up to
$1.65$ GeV, $s$-channel $N^{*}(1535)$ resonance plays the dominant role. The
effect from nucleon pole is found to be small but the interference terms
between the $N^*(1535)$ resonance and the nucleon pole are significant. The
contributions from $t$-channel processes are negligible in the present
calculation.
