  The minimal extension of the MSSM (NMSSM) has been widely studied in the
search for a natural solution to the $\mu$ problem. In this work, we consider a
variation of the NMSSM where an extra singlet is added and a Peccei-Quinn
symmetry is imposed. We study its neutralino sector and compute the
annihilation cross section of the lightest neutralino. We use existent
cosmological and collider data to constrain the parameter space and consider
the lightest neutralino, which is very light, as a dark matter candidate.
