  We propose a model of inflation based on a simple variant of the NMSSM,
called $\phi$NMSSM where the additional singlet $\phi$ plays the role of the
inflaton in hybrid (or inverted hybrid) type models. The $\phi$NMSSM solves the
$\mu$ problem of the MSSM via the vacuum expectation value of the gauge singlet
N, but also solves the strong CP problem through an approximate Peccei-Quinn
symmetry. The potential energy which drives inflation originates from the
F-term of the effective supergravity theory which result from a generic string
theory. In the class of models considered the inflaton is protected from
receiving mass during inflation by a Heisenberg symmetry, avoiding the $\eta$
problem.
