We calculated the binding energy per baryon of the Λ hypernuclei systematically, using the relativistic mean field theory(RMF) in a static frame. Some similar properties are found for most of the Λ hypernuclei confirmed by experiments. The data show that a Λ hypernucleus will be more stable, if it is made by adding a Λ hyperon to a stable normal nuclear core, or by replacing a neutron by a Λ hyperon to a stable normal nuclear core. According to our calculations, existences of some new Λ hypernuclei are predicted under the frame of RMF.PACS:21.80.+a, 21.10.DrThe discovery of the strangeness opens a new research field of nuclear physics with strangeness. The research on the structure and property of hypernuclei had produced many meaningful results in 1970s. Some methods, for example, the nuclear core model, RMF and Hartree-Fock-Bogolinbov (HFB), have been used. It has been more than 50 years since the first discovery of a Λ hypernuclei by Polish physicists Marion Danysz and Jerzy Pniewski. [1,2] There has been great progress in understanding Λ hypernuclei since 1970s in experiment and theory. The hypernuclei properties include the hyperon binding energy B Λ [3] , the well depth of Λ-nuclear potential, hypernuclear spins and life times, Λ hypernuclei spectroscopy [4] , the shrinkage of Λ hypernuclear size, π 0 -and π + -mesonic decays, excited states of hypernuclei and binding energy per baryon, etc have been studied. Up to now, 53 hypernuclei have been found, including 40 single-Λ hypernuclei, 3 double-Λ hypernuclei, 8 Ξ − hypernuclei and 2 Σ hypernuclei 4 Σ 0 He, 4 Σ + He [5−−9] . A lot of experimental data has been accumulated. Systematic studies on the binding energy of Λ hypernuclei are required. Sandulescu et al. [10] have used the RMF-BCS approach to treat the resonant states. They considered the resonant states by the scattering states located in the vicinity of the resonance energies, and found that including into the RMF-BCS calculations, only one of these resonant states gets for the neutron radii, and neutron separation energies are practically as same as in the more involved relativistic-Hartree-Bogolinbov (RHB) calculations.As a convenient method, relativistic mean field(RMF) theory can be used to study nuclear many-body systems. It has been widely adopted in predicting the properties of nuclear matter and finite nuclei, not only normal nuclei but also many kinds of hypernuclei. [11−−13] One of the important aspects in RMF is to determine the effective meson-baryon couplings. In this work, we choose NL-SH [14] as the parameters of the meson-baryon coupling constants, which can well describe the properties of finite nuclei and hypernuclei. [11−−13] Under this *