The exciton dynamics in molecular aggregate models composed of triangular lattice units have been investigated using the quantum master equation approach including relaxation terms originating in weak exciton−phonon coupling. We observe directed migration and recurrence motion of exciton after the irradiation of a laser field. It is found that the triangular lattice aggregates tend to suppress the decoherence behavior and thus to exhibit more distinguished longer-term exciton recurrence than the similar size dendritic aggregates, although the former show less efficient exciton migration, that is, light-harvesting behavior, than the latter. These dynamical features of exciton in the triangular lattice aggregate models turned out to be characterized by the strong interactions among spatially close-packed monomers through the branching points, originating in the equilateral triangular structure, as well as by the fractal, tournament-like, architecture.