Photonic and plasmonic quasicrystals, comprising well-designed and regularly-arranged patterns but lacking spatial translational symmetry, show sharp diffraction patterns resulting from their long-range order in spatial domain. Here we demonstrate that plasmonic structure, which is macroscopically arranged with spatial periodicity and microscopically constructed by random metal nanostructures, can also exhibit the diffraction effect experimentally, despite both of the translational symmetry and long-range order are broken in spatial domain simultaneously. With strategically pre-formed metal nano-seeds, the tunable macroscopically periodic (macro-periodic) pattern composed from microscopically random (micro-random) nanoplate-based silver structures are fabricated chemically through photon driven growth using simple light source with low photon energy and low optical power density. The geometry of the micro-structure can be further modified through simple thermal annealing. While the random metal nanostructures suppress high-order Floquet spectra of the spatial distribution of refractive indices, the maintained low-order Floquet spectra after the ensemble averaging are responsible for the observed diffraction effect. A theoretical approach has also been established to describe and understand the macro-periodic and micro-random structures with different micro-geometries. The easy fabrication and comprehensive understanding of this metal structure will be beneficial for its application in plasmonics, photonics and optoelectronics.