The time evolutions of the entanglement between a two-level atom and its spontaneous emission field in free space, cavity, isotropic and anisotropic photonic crystal are studied by using quantum entropy. It is found that the evolution properties of the atom-field entanglement are directly related to the nature of the structured reservoir,specifically, to the distribution of the density of modes. In free space and cavity, as the density of the modes varies smoothly with frequency, the atom-field entanglement decays to zero in a finite time. However in an isotropic and anisotropic photonic crystal, the atom-field entanglement can keep steady due to the existence of a photonic band gap in the density of the modes. Thus, we can control the time evolution of the entanglement between the atom and its spontaneous emission field by changing the density of the modes of the structured reservoirs.