A mechanism for the accumulation of floating marine debris in the North Pacific, especially north of the Hawaiian Islands, is investigated. First, about 50 pseudo marine debris markers floating at the sea surface are arranged in the North Pacific. Their trajectories are simulated by surface currents consisting of Stokes drift, Ekman drift, and geostrophic currents. The simulation by Ekman drift alone shows remarkable convergence at midlatitudes and moderate convergence north of the Hawaiian Islands. On the other hand, that by Stokes drift or geostrophic currents does not present any remarkable high-density area and shows basin-scale movement of marine debris. However, from the simulation by combined surface currents, marine debris gathers north of the Hawaiian Islands. This can be explained by a simple mechanism consisting of a three-step process. First, marine debris accumulates in the Ekman convergence zone related to westerly and trade winds. Second, the debris moves eastward by geostrophic currents. Finally, the debris accumulates north of the Hawaiian Islands by Ekman drift due to the atmospheric North Pacific subtropical high.