  We discuss constraints from cosmology on the models with direct gauge
mediation based on the ISS supersymmetry breaking models. It is a generic
feature that the ISS models possess a U(1) symmetry which is eventually
spontaneously broken, when the models are based on the gauge symmetries with
complex representations. We show that the resultant pseudo Nambu-Goldstone
boson causes problems in cosmology, which leads to severe constraints on the
models. We also show that most parameter space of the models can be probed by
observing gravitational waves emitted from the cosmic string network when the
U(1) symmetry is a gauge symmetry.
