We report here the lateral epitaxial overgrowth (LEO) of GaN on a patterned GaN-on-silicon substrate by molecular beam epitaxy (MBE) growth with radio frequency nitrogen plasma as a gas source. Two kinds of GaN nanostructures are defined by electron beam lithography and realized on a GaN substrate by fast atom beam etching. The epitaxial growth of GaN by MBE is performed on the prepared GaN template, and the selective growth of GaN takes place with the assistance of GaN nanostructures. The LEO of GaN produces novel GaN epitaxial structures which are dependent on the shape and the size of the processed GaN nanostructures. Periodic GaN hexagonal pyramids are generated inside the air holes, and GaN epitaxial strips with triangular section are formed in the grating region. This work provides a promising way for producing novel GaN-based devices by the LEO of GaN using the MBE technique.