We develop a shape-based coarse-grained (SBCG) model for DNA-functionalized gold nanoparticles (DNA-Au NPs) and use this to study the interaction of this potential antisense therapeutic with a lipid bilayer model of a cell membrane that is also represented using a coarse-grained model. Molecular dynamics simulations of the SBCG model of the DNA-Au NP show structural properties which coincide with our previous atomistic models of this system. The lipid membrane is composed of 30% negatively charged lipid (1,2-dioleoyl-sn-glycero-3-phosphoserine, DOPS) and 70% neutral lipid (1,2-dioleoyl-sn-glycero-3-phosphocholine, DOPC) in 0.15 M sodium chloride solution. Molecular dynamics (MD) simulations of the DNA-Au NP near to the lipid bilayer show that there is a higher density of DOPS than DOPC near to the DNA-Au NP since sodium counterions are able to have strong electrostatic interactions with DOPS and the DNA-Au NP at the same time. Using a steered MD simulation, we show that this counterion-mediated electrostatic interaction between DNA-Au NP and DOPS stabilizes the DNA-Au NP in direct contact with the lipid. This provides a model for interaction of DNA-Au NPs with cell membranes that does not require protein mediation.