This research theoretically investigates the emergence of nested structures in plankton patchiness. Considering the vertical migration of plankton populations, we develop a spatiotemporal dynamic model that describes the coupling of two phytoplankton-zooplankton systems. The conditions of pattern self-organization are derived, and importantly, the dispersion relation with two peaks is found to be the key for the occurrence of nested patterns. Based on the analysis of amplitude equations and simulations, four cases of nested patterns that are characterized by the nestedness of different sizes of hexagon and stripe patches are found. As the ratio of the wavenumbers corresponding to the critical Turing modes of patterns increases, the difference of patch sizes in the nested structures rises accordingly, leading to more small patches growing in the large ones. Moreover, the effect of advection on the self-organization of nested patterns is also discussed. The findings in this research may contribute to a new comprehension of the nestedness phenomenon occurring in the spatial distribution of plankton, as observed in field investigations.