  We study the neutralino sector of the Minimal Non-minimal Supersymmetric
Standard Model (MNSSM) where the $\mu$ problem of the Minimal Supersymmetric
Standard Model (MSSM) is solved without accompanying problems related with the
appearance of domain walls. In the MNSSM as in the MSSM the lightest neutralino
can be the absolutely stable lightest supersymmetric particle (LSP) providing a
good candidate for the cold dark matter component of the Universe. In contrast
with the MSSM the allowed range of the mass of the lightest neutralino in the
MNSSM is limited. We establish the theoretical upper bound on the lightest
neutralino mass in the framework of this model and obtain an approximate
solution for this mass.
