In this article, the Green Function method has been employed to investigate the infrared spectrum of one-dimensional twobloek crystal A-E. Assuming that the Green Functions of the blocks are known, we first derive the matrices and the Green Functions of the crystal and then investigate some quantities important to infrared spectrum of the crystal, including (1) the density of states, (2) the eigenfrequencies of the crystal, (3) the normal displacements of atoms in the crystal, (4) infrared absorption intensity and (5) peak width.