We deduce a two-level model of light propagating in photonic lattices of Kerr medium and two kinds of saturated photorefractive medium,establish the classical Hamiltonian system, study the evolution of the phase-space motion of the Hamiltonian system for one kind of saturated photorefractive medium, namely, the Screening medium, and then study the nonlinear Landau-Zener tunneling numerically. Results show that the tunneling probability is enhanced when the nonlinearity is positive while it is restrained when the nonlinearity is negative.