  We have investigated the strong gravitational lensing for the photons coupled
to Weyl tensor in a Schwarzschild black hole spacetime. We find that in the
four-dimensional black hole spacetime the equation of motion of the photons
depends not only on the coupling between photon and Weyl tensor, but also on
the polarization direction of the photons. It is quite different from that in
the case of the usual photon without coupling to Weyl tensor in which the
equation of motion is independent of the polarization of the photon. Moreover,
we find that the coupling and the polarization direction modify the properties
of the photon sphere, the deflection angle, the coefficients in strong field
lensing, and the observational gravitational lensing variables. Combining with
the supermassive central object in our Galaxy, we estimated three observables
in the strong gravitational lensing for the photons coupled to Weyl tensor.
