The supersymmetric (SUSY) $E_6$ inspired $U(1)_N$ extension of the Standard Model includes exotic fermions to ensure anomaly cancellation. The cold dark matter in this SUSY model (SE$_6$SSM)
can be formed by the gravitino with mass $m_{3/2}\lesssim 1\,\mbox{GeV}$ and the lightest neutral exotic fermion. We examine the spin-independent dark matter nucleon scattering cross-section within the SE$_6$SSM and argue that it can be substantially smaller than the current experimental bounds.