Based on the exact periodic and soliton solution, the modulation instability (MI) of nonlinear optical lattice with an
elliptic function potential has been investigated. The general perturbation coupled equations based on the solutions were
obtained, and then were solved by numerical method. It can be found that the perturbation can be affected by the
parameters of the optical lattice because the soliton solution depends sensitively on the optical lattice. The modulation
depth V affects the amplitude of gain spectrum, while modulation periodic κ affects both the amplitude and fastest
growth frequency of gain spectrum.