  We investigate cosmological moduli problem in the gauge-mediated
supersymmetry breaking (GMSB). A mini-inflation (oscillating inflation) takes
place when a scalar field corresponding to the flat direction in GMSB
oscillates along the logarithmic potential induced by the gauge-mediation
mechanism. It is shown that this oscillating inflation can sufficiently dilute
the relic abundance of the string moduli for some ranges of parameters in the
GMSB models.
