  Konoplya and Zhidenko have proposed recently a rotating non-Kerr black hole
metric beyond General Relativity and make an estimate for the possible
deviations from the Kerr solution with the data of GW 150914. We here study the
strong gravitational lensing in such a rotating non-Kerr spacetime with an
extra deformation parameter. We find that the condition of existence of
horizons is not inconsistent with that of the marginally circular photon orbit.
Moreover, the deflection angle of the light ray near the weakly naked
singularity covered by the marginally circular orbit diverges logarithmically
in the strong-field limit. In the case of the completely naked singularity, the
deflection angle near the singularity tends to a certain finite value, whose
sign depends on the rotation parameter and the deformation parameter. These
properties of strong gravitational lensing are different from those in the
Johannsen-Psaltis rotating non-Kerr spacetime and in the Janis-Newman-Winicour
spacetime. Modeling the supermassive central object of the Milk Way Galaxy as a
Konoplya-Zhidenko rotating non-Kerr compact object, we estimated the numerical
values of observables for the strong gravitational lensing including the time
delay between two relativistic images.
