The transport of biomolecules across cell boundaries is central to cellular function. While structures of many membrane channels are known, the permeation mechanism is known only for a select few. Molecular dynamics (MD) is a computational method that can provide an accurate description of permeation events at the atomic level, which is required for understanding the transport mechanism. However, due to the relatively short time scales accessible to this method, it is of limited utility. Here, we present a method for all-atom simulation of electric field-driven transport of large solutes through membrane channels, which in tens of nanoseconds can provide a realistic account of a permeation event that would require a millisecond simulation using conventional MD. In this method, the average distribution of the electrostatic potential in a membrane channel under a transmembrane bias of interest is determined first from an all-atom MD simulation. This electrostatic potential, defined on a grid, is subsequently applied to a charged solute to steer its permeation through the membrane channel. We apply this method to investigate permeation of DNA strands, DNA hairpins, and alpha-helical peptides through alpha-hemolysin. To test the accuracy of the method, we computed the relative permeation rates of DNA strands having different sequences and global orientations. The results of the G-SMD simulations were found to be in good agreement in experiment.