  To solve the `TeV gamma crisis', we examine a model whose one spatial
direction is discretized at a high energy scale. Assuming the standard
extra-galactic IR photon distribution, we evaluate the mean free-path of a
energetic photon which acquires an effective mass in the model. For a wide
range of the value of the lattice energy scale between a few TeV and around
$10^{10}$ GeV, the mean free-path of a TeV energy photon can be enlarged enough
to solve the `crisis'. Taking into account the effects of the universe
expansion, we find bounds of the lattice constant.
