The orientation- and position-controlled synthesis of single-crystal topological insulator (Bi2Se3 and Bi2Te3) nanoplate arrays on mica substrates was achieved using van der Waals epitaxy. Individual ultrathin nano-plates with the lateral dimension up to similar to 0.1 mm or uniform thickness down to 1-2 nm were produced. Single-Dirac-cone surface states of nanoplate aggregates were confirmed by angle-resolved photoemission spectroscopy measurements. The large-grain-size, single-crystal nanoplate arrays grown on mica can act as facile platforms for a combination of spectroscopy and in situ transport measurements, which may open up new avenues for studying exotic physical phenomena, surface chemical reactions, and modification in topological insulators.