We theoretically reveal the absorption properties of a 1D periodic structure associated with alternating 3D Dirac semimetals and dielectric layers. The absorption spectra of this structure under both TM and TE polarized waves have been shown, where greatly enhanced absorption is achieved at a certain angle under the TM wave because of the zero effective perpendicular permittivity of the periodic structure. We also reveal that the absorption behavior in this structure can be engineered by the thicknesses of the 3D Dirac semimetal film and the dielectric layer in the unit cell of the periodic structure. In contrast to conventional absorbers made of the metals, the absorption in this periodic structure is highly controllable by the Fermi energy of 3D Dirac semimetals. Our results provide an alternative route to control absorption using 3D Dirac semimetals, which offers alternative options for possible device applications.