Aromatic stacks formed through self-assembly are promising building blocks for the construction Of molecular electronic devices with adjustable electronic functions, in which noncovalently bound pi-stacks act as replaceable modular components. Here we describe the electron-transport properties of single-molecule aromatic stacks aligned in a self-assembled cage, using scanning probe microscopic and break junction methods. Same and different modular aromatic pairs are noncovalently bound and stacked within the molecular cage holder, which leads to diverse electronic functions. The insertion of same pairs induces high electronic conductivity (10(-3)-10(-2) G(0), G(0) = 2e(2)/h), while different pairs develop additional electronic rectification properties. The rectification ratio was, respectively, estimated to be 1.4-2 and >10 in current voltage characteristics and molecular orientation-dependent conductance measurements at a fixed bias voltage. Theoretical calculations demonstrate that this rectification behavior originates from the distinct stacking order of the internal aromatic components against the electron-transport direction and the corresponding lowest unoccupied molecular orbital conduction channels localized on one side of the molecular junctions.