In this work, stoichiometric separate bismuth selenide (Bi2Se3) nanoplates and continuous Bi2Se3 coatings are synthesized on graphene substrate by catalyst-free vapor-solid deposition method. The orientation of synthesized nanoplates relative to the substrate surface varies from heteroepitaxial (planar) to oriented under different angles (non-planar). The non-planar growth of the nanoplates was achieved for the first time by short-term carrier inert gas flow in certain temperature interval of the synthesis process. The crystallographic growth directions of non-planar nanoplates were determined from HRTEM images as well as estimated from the slope angles of non-planar nanoplates. Bi2Se3 coatings consisting of combination of planar and non-planar nanoplates exhibit significantly enhanced in comparison with coating consisting of only planar coalescent Bi2Se3 nanoplates thermoelectric properties. Demonstrated graphene/Bi2Se3/graphene devices may find applications in thermoelectric and photo-detection sensors.