  We present a simple model of gauge mediated supersymmetry breaking with
composite messenger fields. Our model is based on the gauge group $Sp(8) \times
SU(2)$. By the strong Sp(8) dynamics, supersymmetry is dynamically broken and
the composite fields with charges under the standard model gauge group appear
at low energy. The $U(1)_R$ symmetry breaking mass terms for the composite
fields are generated by the strong SU(2) dynamics. Then, the composite fields
play a role of the messenger fields. On the other hand, the theoretical bounds
on the parameters in our model are discussed. Especially, the lower bound on
the dynamical scale of the $Sp(8) \times SU(2)$ gauge interaction is roughly
$10^{15}$ GeV.
