  We study the strong gravitational lensing on the equatorial plane of a
quasi-Kerr compact object with arbitrary quadrupole moments which can be used
to model the super-massive central object of the galaxy. We find that, when the
quadrupolar correction parameter $\xi$ takes the positive (negative) value, the
photon-sphere radius $r_{ps}$, the minimum impact parameter $u_{ps}$, the
coefficient $\bar{b}$, the relative magnitudes $r_m$ and the angular position
of the relativistic images $\theta_{\infty}$ are larger (smaller) than the
results obtained in the Kerr black hole, but the coefficient $\bar{a}$, the
deflection angle $\alpha(\theta)$ and the angular separation $s$ are smaller
(larger) than that in the Kerr black hole. These features may offer a way to
probe special properties for some rotating compact objects by the astronomical
instruments in the future.
