The structure relationship of the As precipitates found in post-annealed Si delta-doped GaAs layers grown by low-temperature molecular beam epitaxy is elucidated by transmission electron microscopy (TEM). There are six extra spots around the diffraction pattern of GaAs for a sample annealed at 700 degrees C. The As precipitates and GaAs matrix are found to be semicoherent with the hexagonal [-1-21](As) parallel to the cubic (GaAs). Because of the different lattice constants and Bravias lattices between GaAs and As precipitates, these extra spots are formed by double-diffraction effects. The high-resolution TEM images show two types of Moire fringes. One is the parallel Moire pattern and the other is the rotation Moire pattern. The relative positions of the extra spots in the diffraction pattern correspond to the orientation and spacing of Moire fringes.