  In this paper, we investigate so-called spherical photon orbits around a
deformed Kerr black hole with an extra deformation parameter. The change in the
azimuth $\Delta\varphi$ and the angle of dragging of nodes per revolution
$\Delta\Omega $ of a complete latitudinal oscillated orbit is calculated
analytically. Finally, representative six examples orbits are plotted out to
illustrate how spherical photon orbits look like and exhibit some interesting
behavior. Especially, this spherical photon orbits are absent in circular
orbits and different from the Kerr case.
