Using a novel rigid body Brownian dynamics algorithm, we investigate how a spherically asymmetrical polyamine molecule, a branched analogue of spermine, interacts with the external vestibule of the voltage-gated potassium channel, Kv1.2. Simulations reveal that the blocker, with a charge of +4e, inserts one of its charged amine groups into the selectivity filter, while another forms a salt bridge with an aspartate residue located just outside the entrance of the pore. This binding mode mimics features of the binding of polypeptides such as the scorpion venom charybdotoxin to the channel. The potential of mean force constructed with Brownian dynamics is a reasonable match to that obtained from molecular dynamics simulations, with dissociation constants of 4.7 and 22 μM, respectively. The current-voltage relationships obtained with and without a blocker in the external reservoir show that the inward current is severely attenuated by the presence of the blocker, whereas the outward current is only moderately reduced. The computational molecular modeling technique we introduce here can provide detailed insights into ligand-channel interactions and can be used for rapidly screening potential blocker molecules.