Atomic spontaneous decay is a fundamental object in quantum optics. It refers to that an atom can jump from its excited state down to its ground state spontaneously due to the vacuum fluctuation, and emits a photon (radiation). Such photon has no steady phase and direction. So the spontaneous decay has no merit to the generation of laser and the coherence of atom and light. In 1946, Purcell suggested that the spontaneous decay can be changed when placing the atom into a cavity. One found the spontaneous decay is not only the inherent character of atom itself, but also depends on the environment surrounding the atom. If the mode density of the environment is zero, the spontaneous decay of atom being in it will be inhibited completely. Then, to find and fabricate structure to control the atomic decay became a hot object. Beside the micro-cavity and micro-guider, in 1987, Yablonovitch and John suggested that the structure arrayed periodically by the different dielectric materials can control atomic spontaneous decay. Then a new research region named photonic crystal come into being. In recent years, a new fabricated material called left-handed materials (LHM) attracts a great deal of attention. Such materials have negative permittivity, permeability and refractive index and still obey the Maxwell equations. With the help of its negative refraction and phase compensation effect, there are great amount of progresses for the application of left-handed material, including the perfect lens, zero average refractive index gap and sub-wavelength cavity, and so on.In this paper, we mainly discus the influence of one-dimension structure containing the left-handed material on the spontaneous decay, including the distribution of radiative field, the spontaneous decay rate and the dynamic decay process.In Section 2, the influence of the multi-layer structure containing LHM on the distribution of radiated field is investigated. Under the condition of impedance-matching, the radiated field is focused in each layer and propagates along the direction normal to each layer due to the negative refraction. With such a structure we can control the propagation of the SpE field without changing the SpE rate.In Section 3, the spontaneous emission of the two-level atom located in a multi-layer structure containing LHM has been studied, and the results are compared