A theoretical framework is presented to model ion and DNA translocation across a nanopore confinement under an applied electric field. A combined Grand Canonical Monte Carlo Brownian Dynamics (GCMC/BD) algorithm offers a general approach to study ion permeation through wide molecular pores with a direct account of ion-ion and ion-DNA correlations. This work extends previously developed theory by incorporating the recently developed coarse-grain polymer model of DNA by de Pablo and colleagues [Knotts, T. A.; Rathore, N.; Schwartz, D. C.; de Pablo, J. J. J. Chem. Phys. 2007, 126] with explicit ions for simulations of polymer dynamics. Atomistic MD simulations were used to guide model developments. The power of the developed scheme is illustrated with studies of single-stranded DNA (ss-DNA) oligomer translocation in two model cases: a cylindrical pore with a varying radius and a well-studied experimental system, the staphylococcal α-hemolysin channel. The developed model shows good agreement with experimental data for model studies of two homopolymers: ss-poly(dA)(n) and ss-poly(dC)(n). The developed protocol allows for direct evaluation of different factors (charge distribution and pore shape and size) controlling DNA translocation in a variety of nanopores.