We report here the synthesis of nano-zeolite, viz., ZSM-5 with MFI topology, having a unique brain-coral morphology, designated as n-ZSM-5. These nanoscopic structures (250-300 nm) are in turn formed by self-organization of uniform nanoparticles of zeolite nanospheres of sizes 10-40 nm. Such a remarkable crystal architecture endows the material with improved physico-chemical properties, viz., enhanced surface area, distributed acid sites, mesoporosity and reduced diffusion resistance, which make n-ZSM-5 a promising solid acid catalyst. For comparison, bulk or conventional ZSM-5, referred to as c-ZSM-5, was also synthesized and its performance for tertiary butylation of phenol was evaluated. Density functional theory modelling studies provide an adequate description of the variation of acid strength observed in temperature-programmed desorption of ammonia experiments. © 2020 The Royal Society of Chemistry.