  We study the cosmological gravitino production in gauge mediated
supersymmetry breaking models, while properly taking into account the existence
of the messenger mass scale. It is found that for sizable parameter range of
the model the messenger sector contribution leads to more stringent upper bound
on the reheat temperature obtained from the condition that the universe should
not be overclosed by relic gravitinos. However it turns out that in the limit
of relatively low messenger scale and large gravitino mass, the relic gravitino
mass density can be smaller than the critical density independently of the
reheat temperature, suggesting the possibility in this limit to have a high
reheat temperature without the dilution of gravitinos at late time.
