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 1 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.